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index 00000000..c5b643dd --- /dev/null +++ b/__site/assets/getting-started/ensembles-3/code/ex1.jl @@ -0,0 +1,3 @@ +# This file was generated, do not modify it. # hide +using MLJ, PyPlot +import Statistics \ No newline at end of file diff --git a/__site/assets/getting-started/ensembles-3/code/ex2.jl b/__site/assets/getting-started/ensembles-3/code/ex2.jl new file mode 100644 index 00000000..20a80b77 --- /dev/null +++ b/__site/assets/getting-started/ensembles-3/code/ex2.jl @@ -0,0 +1,8 @@ +# This file was generated, do not modify it. # hide +Xs = source() +ys = source(kind=:target) + +atom = @load DecisionTreeRegressor +atom.n_subfeatures = 4 # to ensure diversity among trained atomic models + +machines = (machine(atom, Xs, ys) for i in 1:100) \ No newline at end of file diff --git a/__site/assets/getting-started/ensembles-3/code/ex3.jl b/__site/assets/getting-started/ensembles-3/code/ex3.jl new file mode 100644 index 00000000..ff0ffbd7 --- /dev/null +++ b/__site/assets/getting-started/ensembles-3/code/ex3.jl @@ -0,0 +1,5 @@ +# This file was generated, do not modify it. # hide +Statistics.mean(v...) = mean(v) +Statistics.mean(v::AbstractVector{<:AbstractNode}) = node(mean, v...) + +yhat = mean([predict(m, Xs) for m in machines]); \ No newline at end of file diff --git a/__site/assets/getting-started/ensembles-3/code/ex4.jl b/__site/assets/getting-started/ensembles-3/code/ex4.jl new file mode 100644 index 00000000..977e693e --- /dev/null +++ b/__site/assets/getting-started/ensembles-3/code/ex4.jl @@ -0,0 +1,2 @@ +# This file was generated, do not modify it. # hide +one_hundred_models = @from_network OneHundredModels(atom=atom) <= yhat \ No newline at end of file diff --git a/__site/assets/getting-started/ensembles-3/code/ex5.jl b/__site/assets/getting-started/ensembles-3/code/ex5.jl new file mode 100644 index 00000000..ab9dcb86 --- /dev/null +++ b/__site/assets/getting-started/ensembles-3/code/ex5.jl @@ -0,0 +1,2 @@ +# This file was generated, do not modify it. # hide +X, y = @load_boston; \ No newline at end of file diff --git a/__site/assets/getting-started/ensembles-3/code/ex6.jl b/__site/assets/getting-started/ensembles-3/code/ex6.jl new file mode 100644 index 00000000..7c4ce013 --- /dev/null +++ b/__site/assets/getting-started/ensembles-3/code/ex6.jl @@ -0,0 +1,18 @@ +# This file was generated, do not modify it. # hide +r = range(atom, + :min_samples_split, + lower=2, + upper=100, scale=:log) + +mach = machine(atom, X, y) + +curve = learning_curve!(mach, + range=r, + measure=mav, + resampling=CV(nfolds=9), + verbosity=0) + +plot(curve.parameter_values, curve.measurements) +xlabel(curve.parameter_name) + +savefig(joinpath(@OUTPUT, "e1.svg")) # hide \ No newline at end of file diff --git a/__site/assets/getting-started/ensembles-3/code/ex7.jl b/__site/assets/getting-started/ensembles-3/code/ex7.jl new file mode 100644 index 00000000..b6df5ed6 --- /dev/null +++ b/__site/assets/getting-started/ensembles-3/code/ex7.jl @@ -0,0 +1,18 @@ +# This file was generated, do not modify it. # hide +r = range(one_hundred_models, + :(atom.min_samples_split), + lower=2, + upper=100, scale=:log) + +mach = machine(one_hundred_models, X, y) + +curve = learning_curve!(mach, + range=r, + measure=mav, + resampling=CV(nfolds=9), + verbosity=0) + +plot(curve.parameter_values, curve.measurements) +xlabel(curve.parameter_name) + +savefig(joinpath(@OUTPUT, "e2.svg")) # hide \ No newline at end of file diff --git a/__site/assets/getting-started/ensembles-3/code/ex8.jl b/__site/assets/getting-started/ensembles-3/code/ex8.jl new file mode 100644 index 00000000..db395e38 --- /dev/null +++ b/__site/assets/getting-started/ensembles-3/code/ex8.jl @@ -0,0 +1,2 @@ +# This file was generated, do not modify it. # hide +PyPlot.close_figs() # hide \ No newline at end of file diff --git a/__site/assets/getting-started/ensembles-3/code/output/e1.svg b/__site/assets/getting-started/ensembles-3/code/output/e1.svg new file mode 100644 index 00000000..d10ba432 --- /dev/null +++ b/__site/assets/getting-started/ensembles-3/code/output/e1.svg @@ -0,0 +1,754 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/__site/assets/getting-started/ensembles-3/code/output/e2.svg b/__site/assets/getting-started/ensembles-3/code/output/e2.svg new file mode 100644 index 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diff --git a/__site/assets/getting-started/ensembles-3/code/output/ex1.res b/__site/assets/getting-started/ensembles-3/code/output/ex1.res new file mode 100644 index 00000000..97896a0b --- /dev/null +++ b/__site/assets/getting-started/ensembles-3/code/output/ex1.res @@ -0,0 +1 @@ +nothing \ No newline at end of file diff --git a/__site/assets/getting-started/ensembles-3/code/output/ex2.out b/__site/assets/getting-started/ensembles-3/code/output/ex2.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/ensembles-3/code/output/ex2.res b/__site/assets/getting-started/ensembles-3/code/output/ex2.res new file mode 100644 index 00000000..d112101d --- /dev/null +++ b/__site/assets/getting-started/ensembles-3/code/output/ex2.res @@ -0,0 +1 @@ +Base.Generator{UnitRange{Int64},Main.FD_SANDBOX_15866893453267974565.var"#1#2"}(Main.FD_SANDBOX_15866893453267974565.var"#1#2"(), 1:100) \ No newline at end of file diff --git a/__site/assets/getting-started/ensembles-3/code/output/ex3.out b/__site/assets/getting-started/ensembles-3/code/output/ex3.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/ensembles-3/code/output/ex3.res b/__site/assets/getting-started/ensembles-3/code/output/ex3.res new file mode 100644 index 00000000..97896a0b --- /dev/null +++ b/__site/assets/getting-started/ensembles-3/code/output/ex3.res @@ -0,0 +1 @@ +nothing \ No newline at end of file diff --git a/__site/assets/getting-started/ensembles-3/code/output/ex4.out b/__site/assets/getting-started/ensembles-3/code/output/ex4.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/ensembles-3/code/output/ex4.res b/__site/assets/getting-started/ensembles-3/code/output/ex4.res new file mode 100644 index 00000000..266bd6f4 --- /dev/null +++ b/__site/assets/getting-started/ensembles-3/code/output/ex4.res @@ -0,0 +1,9 @@ +OneHundredModels( + atom = DecisionTreeRegressor( + max_depth = -1, + min_samples_leaf = 5, + min_samples_split = 2, + min_purity_increase = 0.0, + n_subfeatures = 4, + post_prune = false, + merge_purity_threshold = 1.0)) @ 1…12 \ No newline at end of file diff --git a/__site/assets/getting-started/ensembles-3/code/output/ex5.out b/__site/assets/getting-started/ensembles-3/code/output/ex5.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/ensembles-3/code/output/ex5.res b/__site/assets/getting-started/ensembles-3/code/output/ex5.res new file mode 100644 index 00000000..97896a0b --- /dev/null +++ b/__site/assets/getting-started/ensembles-3/code/output/ex5.res @@ -0,0 +1 @@ +nothing \ No newline at end of file diff --git a/__site/assets/getting-started/ensembles-3/code/output/ex6.out b/__site/assets/getting-started/ensembles-3/code/output/ex6.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/ensembles-3/code/output/ex6.res 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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/__site/assets/getting-started/stacking/code/ex1.jl b/__site/assets/getting-started/stacking/code/ex1.jl new file mode 100644 index 00000000..5355d495 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex1.jl @@ -0,0 +1,5 @@ +# This file was generated, do not modify it. # hide +using MLJ, PyPlot +MLJ.color_off() # hide +import Random.seed! +seed!(1234) \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex10.jl b/__site/assets/getting-started/stacking/code/ex10.jl new file mode 100644 index 00000000..09d1592d --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex10.jl @@ -0,0 +1,5 @@ +# This file was generated, do not modify it. # hide +MLJ.restrict(X::AbstractNode, f::AbstractNode, i) = + node((XX, ff) -> restrict(XX, ff, i), X, f); +MLJ.corestrict(X::AbstractNode, f::AbstractNode, i) = + node((XX, ff) -> corestrict(XX, ff, i), X, f); \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex11.jl b/__site/assets/getting-started/stacking/code/ex11.jl new file mode 100644 index 00000000..47c3dea5 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex11.jl @@ -0,0 +1,15 @@ +# This file was generated, do not modify it. # hide +figure(figsize=(8,6)) +steps(x) = x < -3/2 ? -1 : (x < 3/2 ? 0 : 1) +x = Float64[-4, -1, 2, -3, 0, 3, -2, 1, 4] +Xraw = (x = x, ) +yraw = steps.(x); +idxsort = sortperm(x) +xsort = x[idxsort] +ysort = yraw[idxsort] +step(xsort, ysort, label="truth", where="mid") +plot(x, yraw, ls="none", marker="o", label="data") +xlim(-4.5, 4.5) +legend() + +savefig(joinpath(@OUTPUT, "s1.svg")) # hide \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex12.jl b/__site/assets/getting-started/stacking/code/ex12.jl new file mode 100644 index 00000000..ce374a7b --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex12.jl @@ -0,0 +1,3 @@ +# This file was generated, do not modify it. # hide +model1 = linear +model2 = knn \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex13.jl b/__site/assets/getting-started/stacking/code/ex13.jl new file mode 100644 index 00000000..c56c5f7d --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex13.jl @@ -0,0 +1,2 @@ +# This file was generated, do not modify it. # hide +judge = linear \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex14.jl b/__site/assets/getting-started/stacking/code/ex14.jl new file mode 100644 index 00000000..8a241026 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex14.jl @@ -0,0 +1,3 @@ +# This file was generated, do not modify it. # hide +X = source(Xraw) +y = source(yraw; kind=:target) \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex15.jl b/__site/assets/getting-started/stacking/code/ex15.jl new file mode 100644 index 00000000..cc355127 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex15.jl @@ -0,0 +1,3 @@ +# This file was generated, do not modify it. # hide +f = folds(X, 3) +f() \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex16.jl b/__site/assets/getting-started/stacking/code/ex16.jl new file mode 100644 index 00000000..159c6fd7 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex16.jl @@ -0,0 +1,4 @@ +# This file was generated, do not modify it. # hide +m11 = machine(model1, corestrict(X, f, 1), corestrict(y, f, 1)) +m12 = machine(model1, corestrict(X, f, 2), corestrict(y, f, 2)) +m13 = machine(model1, corestrict(X, f, 3), corestrict(y, f, 3)) \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex17.jl b/__site/assets/getting-started/stacking/code/ex17.jl new file mode 100644 index 00000000..4d8f4565 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex17.jl @@ -0,0 +1,4 @@ +# This file was generated, do not modify it. # hide +y11 = predict(m11, restrict(X, f, 1)); +y12 = predict(m12, restrict(X, f, 2)); +y13 = predict(m13, restrict(X, f, 3)); \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex18.jl b/__site/assets/getting-started/stacking/code/ex18.jl new file mode 100644 index 00000000..51baca74 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex18.jl @@ -0,0 +1,2 @@ +# This file was generated, do not modify it. # hide +y1_oos = vcat(y11, y12, y13); \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex19.jl b/__site/assets/getting-started/stacking/code/ex19.jl new file mode 100644 index 00000000..d420a147 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex19.jl @@ -0,0 +1,8 @@ +# This file was generated, do not modify it. # hide +fit!(y1_oos, verbosity=0) + +figure(figsize=(8,6)) +step(xsort, ysort, label="truth", where="mid") +plot(x, y1_oos(), ls="none", marker="o", label="linear oos") + +savefig(joinpath(@OUTPUT, "s2.svg")) # hide \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex2.jl b/__site/assets/getting-started/stacking/code/ex2.jl new file mode 100644 index 00000000..4f35af29 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex2.jl @@ -0,0 +1,7 @@ +# This file was generated, do not modify it. # hide +linear = @load LinearRegressor pkg=MLJLinearModels +ridge = @load RidgeRegressor pkg=MultivariateStats; ridge.lambda = 0.01 +knn = @load KNNRegressor; knn.K = 4 +tree = @load DecisionTreeRegressor; min_samples_leaf=1 +forest = @load RandomForestRegressor pkg=DecisionTree; forest.n_trees=500 +svm = @load SVMRegressor; \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex20.jl b/__site/assets/getting-started/stacking/code/ex20.jl new file mode 100644 index 00000000..4d5efce1 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex20.jl @@ -0,0 +1,7 @@ +# This file was generated, do not modify it. # hide +m21 = machine(model2, corestrict(X, f, 1), corestrict(y, f, 1)) +m22 = machine(model2, corestrict(X, f, 2), corestrict(y, f, 2)) +m23 = machine(model2, corestrict(X, f, 3), corestrict(y, f, 3)) +y21 = predict(m21, restrict(X, f, 1)); +y22 = predict(m22, restrict(X, f, 2)); +y23 = predict(m23, restrict(X, f, 3)); \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex21.jl b/__site/assets/getting-started/stacking/code/ex21.jl new file mode 100644 index 00000000..bd959dc8 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex21.jl @@ -0,0 +1,9 @@ +# This file was generated, do not modify it. # hide +y2_oos = vcat(y21, y22, y23); +fit!(y2_oos, verbosity=0) + +figure(figsize=(8,6)) +step(xsort, ysort, label="truth", where="mid") +plot(x, y2_oos(), ls="none", marker="o", label="knn oos") + +savefig(joinpath(@OUTPUT, "s3.svg")) # hide \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex22.jl b/__site/assets/getting-started/stacking/code/ex22.jl new file mode 100644 index 00000000..9456402c --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex22.jl @@ -0,0 +1,3 @@ +# This file was generated, do not modify it. # hide +X_oos = MLJ.table(hcat(y1_oos, y2_oos)) +m_judge = machine(judge, X_oos, y) \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex23.jl b/__site/assets/getting-started/stacking/code/ex23.jl new file mode 100644 index 00000000..503d4899 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex23.jl @@ -0,0 +1,3 @@ +# This file was generated, do not modify it. # hide +m1 = machine(model1, X, y) +m2 = machine(model2, X, y) \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex24.jl b/__site/assets/getting-started/stacking/code/ex24.jl new file mode 100644 index 00000000..ca5df7a7 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex24.jl @@ -0,0 +1,5 @@ +# This file was generated, do not modify it. # hide +y1 = predict(m1, X); +y2 = predict(m2, X); +X_judge = MLJ.table(hcat(y1, y2)) +yhat = predict(m_judge, X_judge) \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex25.jl b/__site/assets/getting-started/stacking/code/ex25.jl new file mode 100644 index 00000000..53d9fab1 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex25.jl @@ -0,0 +1,8 @@ +# This file was generated, do not modify it. # hide +fit!(yhat, verbosity=0) + +figure(figsize=(8,6)) +step(xsort, ysort, label="truth", where="mid") +plot(x, yhat(), ls="none", marker="o", label="yhat") + +savefig(joinpath(@OUTPUT, "s4.svg")) # hide \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex26.jl b/__site/assets/getting-started/stacking/code/ex26.jl new file mode 100644 index 00000000..ecd451d0 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex26.jl @@ -0,0 +1,6 @@ +# This file was generated, do not modify it. # hide +e1 = rms(y1(), y()) +e2 = rms(y2(), y()) +emean = rms(0.5*y1() + 0.5*y2(), y()) +estack = rms(yhat(), y()) +@show e1 e2 emean estack; \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex27.jl b/__site/assets/getting-started/stacking/code/ex27.jl new file mode 100644 index 00000000..8b954d89 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex27.jl @@ -0,0 +1,4 @@ +# This file was generated, do not modify it. # hide +@from_network MyTwoModelStack(regressor1=model1, + regressor2=model2, + judge=judge) <= yhat \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex28.jl b/__site/assets/getting-started/stacking/code/ex28.jl new file mode 100644 index 00000000..e7bba5b1 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex28.jl @@ -0,0 +1,2 @@ +# This file was generated, do not modify it. # hide +X0, y0 = @load_reduced_ames; \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex29.jl b/__site/assets/getting-started/stacking/code/ex29.jl new file mode 100644 index 00000000..593a3ba0 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex29.jl @@ -0,0 +1,3 @@ +# This file was generated, do not modify it. # hide +s = schema(X0) +(names=collect(s.names), scitypes=collect(s.scitypes)) |> pretty \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex3.jl b/__site/assets/getting-started/stacking/code/ex3.jl new file mode 100644 index 00000000..c19a4502 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex3.jl @@ -0,0 +1,14 @@ +# This file was generated, do not modify it. # hide +X = source() +y = source(kind=:target) + +model1 = linear +model2 = knn + +m1 = machine(model1, X, y) +y1 = predict(m1, X) + +m2 = machine(model2, X, y) +y2 = predict(m2, X) + +yhat = 0.5*y1 + 0.5*y2 \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex30.jl b/__site/assets/getting-started/stacking/code/ex30.jl new file mode 100644 index 00000000..697a1135 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex30.jl @@ -0,0 +1,5 @@ +# This file was generated, do not modify it. # hide +X1 = coerce(X0, :OverallQual => Continuous, + :GarageCars => Continuous, + :YearRemodAdd => Continuous, + :YearBuilt => Continuous); \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex31.jl b/__site/assets/getting-started/stacking/code/ex31.jl new file mode 100644 index 00000000..14165850 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex31.jl @@ -0,0 +1,3 @@ +# This file was generated, do not modify it. # hide +hot_mach = fit!(machine(OneHotEncoder(), X1), verbosity=0) +X = transform(hot_mach, X1); \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex32.jl b/__site/assets/getting-started/stacking/code/ex32.jl new file mode 100644 index 00000000..6604a745 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex32.jl @@ -0,0 +1,2 @@ +# This file was generated, do not modify it. # hide +scitype(X) \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex33.jl b/__site/assets/getting-started/stacking/code/ex33.jl new file mode 100644 index 00000000..2a5e3803 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex33.jl @@ -0,0 +1,4 @@ +# This file was generated, do not modify it. # hide +y1 = log.(y0) +y = transform(fit!(machine(UnivariateStandardizer(), y1), + verbosity=0), y1); \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex34.jl b/__site/assets/getting-started/stacking/code/ex34.jl new file mode 100644 index 00000000..50044d10 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex34.jl @@ -0,0 +1,14 @@ +# This file was generated, do not modify it. # hide +avg = MyAverageTwo(regressor1=forest, + regressor2=ridge) + + +stack = MyTwoModelStack(regressor1=forest, + regressor2=ridge, + judge=linear) + +all_models = [forest, ridge, avg, stack]; + +for model in all_models + print_performance(model, X, y) +end; \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex35.jl b/__site/assets/getting-started/stacking/code/ex35.jl new file mode 100644 index 00000000..d2e21434 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex35.jl @@ -0,0 +1,11 @@ +# This file was generated, do not modify it. # hide +r = range(stack, :(regressor2.lambda), lower = 1, upper = 20, scale=:log) +tuned_stack = TunedModel(model=stack, + ranges=r, + tuning=Grid(), + measure=rms, + resampling=Holdout()) + +mach = fit!(machine(tuned_stack, X, y), verbosity=0) +best_stack = fitted_params(mach).best_model +best_stack.regressor2.lambda \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex36.jl b/__site/assets/getting-started/stacking/code/ex36.jl new file mode 100644 index 00000000..02219841 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex36.jl @@ -0,0 +1,4 @@ +# This file was generated, do not modify it. # hide +print_performance(best_stack, X, y) + +PyPlot.close_figs() # hide \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex4.jl b/__site/assets/getting-started/stacking/code/ex4.jl new file mode 100644 index 00000000..bce128ea --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex4.jl @@ -0,0 +1,3 @@ +# This file was generated, do not modify it. # hide +avg = @from_network MyAverageTwo(regressor1=model1, + regressor2=model2) <= yhat \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex5.jl b/__site/assets/getting-started/stacking/code/ex5.jl new file mode 100644 index 00000000..874e0660 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex5.jl @@ -0,0 +1,16 @@ +# This file was generated, do not modify it. # hide +function print_performance(model, data...) + e = evaluate(model, data...; + resampling=CV(rng=1234, nfolds=8), + measure=rms, + verbosity=0) + μ = round(e.measurement[1], sigdigits=5) + ste = round(std(e.per_fold[1])/sqrt(8), digits=5) + println("\n $model = $μ ± $(2*ste)") +end; + +X, y = @load_boston + +print_performance(linear, X, y) +print_performance(knn, X, y) +print_performance(avg, X, y) \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex6.jl b/__site/assets/getting-started/stacking/code/ex6.jl new file mode 100644 index 00000000..e7ca185e --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex6.jl @@ -0,0 +1,3 @@ +# This file was generated, do not modify it. # hide +folds(data, nfolds) = + partition(1:nrows(data), (1/nfolds for i in 1:(nfolds-1))...); \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex7.jl b/__site/assets/getting-started/stacking/code/ex7.jl new file mode 100644 index 00000000..af749c42 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex7.jl @@ -0,0 +1,2 @@ +# This file was generated, do not modify it. # hide +f = folds(1:10, 3) \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex8.jl b/__site/assets/getting-started/stacking/code/ex8.jl new file mode 100644 index 00000000..f54f0a92 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex8.jl @@ -0,0 +1,2 @@ +# This file was generated, do not modify it. # hide +folds(X::AbstractNode, nfolds) = node(XX -> folds(XX, nfolds), X); \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/ex9.jl b/__site/assets/getting-started/stacking/code/ex9.jl new file mode 100644 index 00000000..4dda2f56 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/ex9.jl @@ -0,0 +1,2 @@ +# This file was generated, do not modify it. # hide +corestrict(string.(1:10), f, 2) \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/e1.svg b/__site/assets/getting-started/stacking/code/output/e1.svg new file mode 100644 index 00000000..a7c87fe4 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/e1.svg @@ -0,0 +1,783 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/__site/assets/getting-started/stacking/code/output/ex1.out b/__site/assets/getting-started/stacking/code/output/ex1.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex1.res b/__site/assets/getting-started/stacking/code/output/ex1.res new file mode 100644 index 00000000..840e3910 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex1.res @@ -0,0 +1 @@ +MersenneTwister(UInt32[0x000004d2]) @ 1002 \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex10.out b/__site/assets/getting-started/stacking/code/output/ex10.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex10.res b/__site/assets/getting-started/stacking/code/output/ex10.res new file mode 100644 index 00000000..97896a0b --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex10.res @@ -0,0 +1 @@ +nothing \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex11.out b/__site/assets/getting-started/stacking/code/output/ex11.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex11.res b/__site/assets/getting-started/stacking/code/output/ex11.res new file mode 100644 index 00000000..97896a0b --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex11.res @@ -0,0 +1 @@ +nothing \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex12.out b/__site/assets/getting-started/stacking/code/output/ex12.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex12.res b/__site/assets/getting-started/stacking/code/output/ex12.res new file mode 100644 index 00000000..3a98db3b --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex12.res @@ -0,0 +1,7 @@ +KNNRegressor( + K = 4, + algorithm = :kdtree, + metric = Distances.Euclidean(0.0), + leafsize = 10, + reorder = true, + weights = :uniform) @ 1…34 \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex13.out b/__site/assets/getting-started/stacking/code/output/ex13.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex13.res b/__site/assets/getting-started/stacking/code/output/ex13.res new file mode 100644 index 00000000..72b18687 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex13.res @@ -0,0 +1,3 @@ +LinearRegressor( + fit_intercept = true, + solver = nothing) @ 5…31 \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex14.out b/__site/assets/getting-started/stacking/code/output/ex14.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex14.res b/__site/assets/getting-started/stacking/code/output/ex14.res new file mode 100644 index 00000000..cfc8c6e5 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex14.res @@ -0,0 +1 @@ +Source{:target} @ 1…80 diff --git a/__site/assets/getting-started/stacking/code/output/ex15.out b/__site/assets/getting-started/stacking/code/output/ex15.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex15.res b/__site/assets/getting-started/stacking/code/output/ex15.res new file mode 100644 index 00000000..d88b1bba --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex15.res @@ -0,0 +1 @@ +([1, 2, 3], [4, 5, 6], [7, 8, 9]) \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex16.out b/__site/assets/getting-started/stacking/code/output/ex16.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex16.res b/__site/assets/getting-started/stacking/code/output/ex16.res new file mode 100644 index 00000000..10c1ad73 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex16.res @@ -0,0 +1 @@ +NodalMachine @ 2…93 = machine(LinearRegressor @ 5…31, 8…47, 6…53) \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex17.out b/__site/assets/getting-started/stacking/code/output/ex17.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex17.res b/__site/assets/getting-started/stacking/code/output/ex17.res new file mode 100644 index 00000000..97896a0b --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex17.res @@ -0,0 +1 @@ +nothing \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex18.out b/__site/assets/getting-started/stacking/code/output/ex18.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex18.res b/__site/assets/getting-started/stacking/code/output/ex18.res new file mode 100644 index 00000000..97896a0b --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex18.res @@ -0,0 +1 @@ +nothing \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex19.out b/__site/assets/getting-started/stacking/code/output/ex19.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex19.res b/__site/assets/getting-started/stacking/code/output/ex19.res new file mode 100644 index 00000000..97896a0b --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex19.res @@ -0,0 +1 @@ +nothing \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex2.out b/__site/assets/getting-started/stacking/code/output/ex2.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex2.res b/__site/assets/getting-started/stacking/code/output/ex2.res new file mode 100644 index 00000000..97896a0b --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex2.res @@ -0,0 +1 @@ +nothing \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex20.out b/__site/assets/getting-started/stacking/code/output/ex20.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex20.res b/__site/assets/getting-started/stacking/code/output/ex20.res new file mode 100644 index 00000000..97896a0b --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex20.res @@ -0,0 +1 @@ +nothing \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex21.out b/__site/assets/getting-started/stacking/code/output/ex21.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex21.res b/__site/assets/getting-started/stacking/code/output/ex21.res new file mode 100644 index 00000000..97896a0b --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex21.res @@ -0,0 +1 @@ +nothing \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex22.out b/__site/assets/getting-started/stacking/code/output/ex22.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex22.res b/__site/assets/getting-started/stacking/code/output/ex22.res new file mode 100644 index 00000000..508d0418 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex22.res @@ -0,0 +1 @@ +NodalMachine @ 1…19 = machine(LinearRegressor @ 5…31, 1…60, 1…80) \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex23.out b/__site/assets/getting-started/stacking/code/output/ex23.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex23.res b/__site/assets/getting-started/stacking/code/output/ex23.res new file mode 100644 index 00000000..8b496cd5 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex23.res @@ -0,0 +1 @@ +NodalMachine @ 8…74 = machine(KNNRegressor @ 1…34, 6…44, 1…80) \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex24.out b/__site/assets/getting-started/stacking/code/output/ex24.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex24.res b/__site/assets/getting-started/stacking/code/output/ex24.res new file mode 100644 index 00000000..49f8439c --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex24.res @@ -0,0 +1 @@ +Node @ 4…11 = predict(1…19, table(hcat(predict(1…75, 6…44), predict(8…74, 6…44)))) \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex25.out b/__site/assets/getting-started/stacking/code/output/ex25.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex25.res b/__site/assets/getting-started/stacking/code/output/ex25.res new file mode 100644 index 00000000..97896a0b --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex25.res @@ -0,0 +1 @@ +nothing \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex26.out b/__site/assets/getting-started/stacking/code/output/ex26.out new file mode 100644 index 00000000..7c1f1695 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex26.out @@ -0,0 +1,4 @@ +e1 = 0.2581988897471611 +e2 = 0.25 +emean = 0.22126530078919587 +estack = 0.19577994695380313 diff --git a/__site/assets/getting-started/stacking/code/output/ex26.res b/__site/assets/getting-started/stacking/code/output/ex26.res new file mode 100644 index 00000000..97896a0b --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex26.res @@ -0,0 +1 @@ +nothing \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex27.out b/__site/assets/getting-started/stacking/code/output/ex27.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex27.res b/__site/assets/getting-started/stacking/code/output/ex27.res new file mode 100644 index 00000000..261f295e --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex27.res @@ -0,0 +1,14 @@ +MyTwoModelStack( + regressor1 = LinearRegressor( + fit_intercept = true, + solver = nothing), + regressor2 = KNNRegressor( + K = 4, + algorithm = :kdtree, + metric = Distances.Euclidean(0.0), + leafsize = 10, + reorder = true, + weights = :uniform), + judge = LinearRegressor( + fit_intercept = true, + solver = nothing)) @ 1…65 \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex28.out b/__site/assets/getting-started/stacking/code/output/ex28.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex28.res b/__site/assets/getting-started/stacking/code/output/ex28.res new file mode 100644 index 00000000..97896a0b --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex28.res @@ -0,0 +1 @@ +nothing \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex29.out b/__site/assets/getting-started/stacking/code/output/ex29.out new file mode 100644 index 00000000..775d54d1 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex29.out @@ -0,0 +1,18 @@ +┌──────────────┬───────────────────┐ +│ names │ scitypes │ +│ Symbol │ DataType │ +│ Unknown │ Unknown │ +├──────────────┼───────────────────┤ +│ OverallQual │ OrderedFactor{10} │ +│ GrLivArea │ Continuous │ +│ Neighborhood │ Multiclass{25} │ +│ x1stFlrSF │ Continuous │ +│ TotalBsmtSF │ Continuous │ +│ BsmtFinSF1 │ Continuous │ +│ LotArea │ Continuous │ +│ GarageCars │ Count │ +│ MSSubClass │ Multiclass{15} │ +│ GarageArea │ Continuous │ +│ YearRemodAdd │ Count │ +│ YearBuilt │ Count │ +└──────────────┴───────────────────┘ diff --git a/__site/assets/getting-started/stacking/code/output/ex29.res b/__site/assets/getting-started/stacking/code/output/ex29.res new file mode 100644 index 00000000..97896a0b --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex29.res @@ -0,0 +1 @@ +nothing \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex3.out b/__site/assets/getting-started/stacking/code/output/ex3.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex3.res b/__site/assets/getting-started/stacking/code/output/ex3.res new file mode 100644 index 00000000..594288fc --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex3.res @@ -0,0 +1 @@ +Node @ 7…82 = +(#80(predict(1…58, 2…95)), #80(predict(5…88, 2…95))) \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex30.out b/__site/assets/getting-started/stacking/code/output/ex30.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex30.res b/__site/assets/getting-started/stacking/code/output/ex30.res new file mode 100644 index 00000000..97896a0b --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex30.res @@ -0,0 +1 @@ +nothing \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex31.out b/__site/assets/getting-started/stacking/code/output/ex31.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex31.res b/__site/assets/getting-started/stacking/code/output/ex31.res new file mode 100644 index 00000000..97896a0b --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex31.res @@ -0,0 +1 @@ +nothing \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex32.out b/__site/assets/getting-started/stacking/code/output/ex32.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex32.res b/__site/assets/getting-started/stacking/code/output/ex32.res new file mode 100644 index 00000000..713143ba --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex32.res @@ -0,0 +1 @@ +Table{AbstractArray{Continuous,1}} \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex33.out b/__site/assets/getting-started/stacking/code/output/ex33.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex33.res b/__site/assets/getting-started/stacking/code/output/ex33.res new file mode 100644 index 00000000..97896a0b --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex33.res @@ -0,0 +1 @@ +nothing \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex34.out b/__site/assets/getting-started/stacking/code/output/ex34.out new file mode 100644 index 00000000..2dc2bed9 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex34.out @@ -0,0 +1,8 @@ + + RandomForestRegressor @ 1…05 = 0.3625 ± 0.02022 + + RidgeRegressor @ 1…79 = 0.33029 ± 0.01908 + + MyAverageTwo @ 2…57 = 0.34601 ± 0.01464 + + MyTwoModelStack @ 6…91 = 0.33028 ± 0.01938 diff --git a/__site/assets/getting-started/stacking/code/output/ex34.res b/__site/assets/getting-started/stacking/code/output/ex34.res new file mode 100644 index 00000000..97896a0b --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex34.res @@ -0,0 +1 @@ +nothing \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex35.out b/__site/assets/getting-started/stacking/code/output/ex35.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex35.res b/__site/assets/getting-started/stacking/code/output/ex35.res new file mode 100644 index 00000000..5ac790b5 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex35.res @@ -0,0 +1 @@ +10.27808532802195 \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex36.out b/__site/assets/getting-started/stacking/code/output/ex36.out new file mode 100644 index 00000000..4845786f --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex36.out @@ -0,0 +1,2 @@ + + MyTwoModelStack @ 1…18 = 0.32861 ± 0.01914 diff --git a/__site/assets/getting-started/stacking/code/output/ex36.res b/__site/assets/getting-started/stacking/code/output/ex36.res new file mode 100644 index 00000000..97896a0b --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex36.res @@ -0,0 +1 @@ +nothing \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex4.out b/__site/assets/getting-started/stacking/code/output/ex4.out new file mode 100644 index 00000000..e69de29b diff --git a/__site/assets/getting-started/stacking/code/output/ex4.res b/__site/assets/getting-started/stacking/code/output/ex4.res new file mode 100644 index 00000000..9d1642cf --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex4.res @@ -0,0 +1,11 @@ +MyAverageTwo( + regressor1 = LinearRegressor( + fit_intercept = true, + solver = nothing), + regressor2 = KNNRegressor( + K = 4, + algorithm = :kdtree, + metric = Distances.Euclidean(0.0), + leafsize = 10, + reorder = true, + weights = :uniform)) @ 1…06 \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex5.out b/__site/assets/getting-started/stacking/code/output/ex5.out new file mode 100644 index 00000000..4a96ce4e --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex5.out @@ -0,0 +1,6 @@ + + LinearRegressor @ 5…31 = 4.9779 ± 0.90056 + + KNNRegressor @ 1…34 = 6.3794 ± 0.89744 + + MyAverageTwo @ 1…06 = 4.9802 ± 0.94746 diff --git a/__site/assets/getting-started/stacking/code/output/ex5.res b/__site/assets/getting-started/stacking/code/output/ex5.res new file mode 100644 index 00000000..97896a0b --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/ex5.res @@ -0,0 +1 @@ +nothing \ No newline at end of file diff --git a/__site/assets/getting-started/stacking/code/output/ex6.out b/__site/assets/getting-started/stacking/code/output/ex6.out new file mode 100644 index 00000000..e69de29b diff --git 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00000000..798e2be8 --- /dev/null +++ b/__site/assets/getting-started/stacking/code/output/s4.svg @@ -0,0 +1,472 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/__site/assets/literate/A-ensembles-3.md b/__site/assets/literate/A-ensembles-3.md new file mode 100644 index 00000000..cd572469 --- /dev/null +++ b/__site/assets/literate/A-ensembles-3.md @@ -0,0 +1,103 @@ + +# Simple example of a homogeneous ensemble using learning networks + +In this simple example, no bagging is used, so every atomic model +gets the same learned parameters, unless the atomic model training +algorithm has randomness, eg, DecisionTree with random subsampling +of features at nodes. + +Note that MLJ has a built in model wrapper called `EnsembleModel` +for creating bagged ensembles with a few lines of code. + +## Definition of composite model type + +```julia:ex1 +using MLJ, PyPlot +import Statistics +``` + +learning network (composite model spec): + +```julia:ex2 +Xs = source() +ys = source(kind=:target) + +atom = @load DecisionTreeRegressor +atom.n_subfeatures = 4 # to ensure diversity among trained atomic models + +machines = (machine(atom, Xs, ys) for i in 1:100) +``` + +overload `mean` for nodes: + +```julia:ex3 +Statistics.mean(v...) = mean(v) +Statistics.mean(v::AbstractVector{<:AbstractNode}) = node(mean, v...) + +yhat = mean([predict(m, Xs) for m in machines]); +``` + +new composite model type and instance: + +```julia:ex4 +one_hundred_models = @from_network OneHundredModels(atom=atom) <= yhat +``` + +## Application to data + +```julia:ex5 +X, y = @load_boston; +``` + +tune regularization parameter for a *single* tree: + +```julia:ex6 +r = range(atom, + :min_samples_split, + lower=2, + upper=100, scale=:log) + +mach = machine(atom, X, y) + +curve = learning_curve!(mach, + range=r, + measure=mav, + resampling=CV(nfolds=9), + verbosity=0) + +plot(curve.parameter_values, curve.measurements) +xlabel(curve.parameter_name) + +savefig(joinpath(@OUTPUT, "e1.svg")) # hide +``` + +\fig{e1.svg} + +tune regularization parameter for all trees in ensemble simultaneously: + +```julia:ex7 +r = range(one_hundred_models, + :(atom.min_samples_split), + lower=2, + upper=100, scale=:log) + +mach = machine(one_hundred_models, X, y) + +curve = learning_curve!(mach, + range=r, + measure=mav, + resampling=CV(nfolds=9), + verbosity=0) + +plot(curve.parameter_values, curve.measurements) +xlabel(curve.parameter_name) + +savefig(joinpath(@OUTPUT, "e2.svg")) # hide +``` + +\fig{e2} + +```julia:ex8 +PyPlot.close_figs() # hide +``` + diff --git a/__site/assets/literate/A-ensembles-3_script.jl b/__site/assets/literate/A-ensembles-3_script.jl new file mode 100644 index 00000000..6c75381e --- /dev/null +++ b/__site/assets/literate/A-ensembles-3_script.jl @@ -0,0 +1,60 @@ +# This file was generated, do not modify it. + +using MLJ, PyPlot +import Statistics + +Xs = source() +ys = source(kind=:target) + +atom = @load DecisionTreeRegressor +atom.n_subfeatures = 4 # to ensure diversity among trained atomic models + +machines = (machine(atom, Xs, ys) for i in 1:100) + +Statistics.mean(v...) = mean(v) +Statistics.mean(v::AbstractVector{<:AbstractNode}) = node(mean, v...) + +yhat = mean([predict(m, Xs) for m in machines]); + +one_hundred_models = @from_network OneHundredModels(atom=atom) <= yhat + +X, y = @load_boston; + +r = range(atom, + :min_samples_split, + lower=2, + upper=100, scale=:log) + +mach = machine(atom, X, y) + +curve = learning_curve!(mach, + range=r, + measure=mav, + resampling=CV(nfolds=9), + verbosity=0) + +plot(curve.parameter_values, curve.measurements) +xlabel(curve.parameter_name) + +savefig(joinpath(@OUTPUT, "e1.svg")) # hide + +r = range(one_hundred_models, + :(atom.min_samples_split), + lower=2, + upper=100, scale=:log) + +mach = machine(one_hundred_models, X, y) + +curve = learning_curve!(mach, + range=r, + measure=mav, + resampling=CV(nfolds=9), + verbosity=0) + +plot(curve.parameter_values, curve.measurements) +xlabel(curve.parameter_name) + +savefig(joinpath(@OUTPUT, "e2.svg")) # hide + +PyPlot.close_figs() # hide + diff --git a/__site/assets/literate/A-stacking.md b/__site/assets/literate/A-stacking.md new file mode 100644 index 00000000..0b7f65b2 --- /dev/null +++ b/__site/assets/literate/A-stacking.md @@ -0,0 +1,475 @@ + +In stacking one blends the predictions of different regressors or +classifiers to gain, in some cases, better performance than naive +averaging or majority vote. + +Here we illustrate how to build a two-model stack as an MLJ learning +network, which we export as a new stand-alone composite model +type `MyTwoStack`. This will make the stack that we build completely +re-usable (new data, new models) and means we can apply +meta-algorithms, such as performance evaluation and tuning, to the +stack, exaclty as we would for any other model. + +Our main purpose here is to demonstrate the flexibility of MLJ's +composite model interface. Eventually, MLJ will provide built-in +composite types or macros to achieve the same results in a few +lines, which will suffice for routine stacking tasks. + +After defining the `MyTwoStack` model type, we instantiate it for an +application to the Ames House Price data set. + +## Basic stacking using out-of-sample base learner predictions + +A rather general stacking protocol was first described in a [1992 +paper](https://www.sciencedirect.com/science/article/abs/pii/S0893608005800231) +by David Wolpert. For a generic introduction to the basic two-layer +stack described here, see [this blog +post](https://burakhimmetoglu.com/2016/12/01/stacking-models-for-improved-predictions/) +of Burak Himmetoglu. + +A basic stack consists of a number of base learners (two, in this +illustration) and a single adjudicating model. + +When a stacked model is called to make a prediction, the individual +predictions of the base learners are made the columns of an *input* +table for the adjudicating model, which then outputs the final +prediction. However, it is crucial to understand that the flow of +data *during training* is not the same. + +The base model predictions used to train the adjudicating model are +*not* the predictions of the base learners fitted to all the +training data. Rather, to prevent the adjudicator giving too much +weight to the base learners with low *training* error, the input +data is first split into a number of folds (as in cross-validation), +a base learner is trained on each fold complement individually, and +corresponding predictions on the folds are spliced together to form +a full-length prediction called the *out-of-sample.prediction*. + +For illustrative purposes we use just three folds. Each base learner +will get three separate machines, for training on each fold +complement, and a fourth machine, trained on all the supplied data, +for use in the prediction flow. + +We build the learning network with dummy data at the source nodes, +so the reader inspect the workings of the network as it is built (by +calling `fit!` on nodes, and by calling the nodes themselves). As +usual, this data is not seen by the exported composite model type, +and the component models we choose are just default values for the +hyperparameters of the composite model. + +```julia:ex1 +using MLJ, PyPlot +MLJ.color_off() # hide +import Random.seed! +seed!(1234) +``` + +Some models we will use: + +```julia:ex2 +linear = @load LinearRegressor pkg=MLJLinearModels +ridge = @load RidgeRegressor pkg=MultivariateStats; ridge.lambda = 0.01 +knn = @load KNNRegressor; knn.K = 4 +tree = @load DecisionTreeRegressor; min_samples_leaf=1 +forest = @load RandomForestRegressor pkg=DecisionTree; forest.n_trees=500 +svm = @load SVMRegressor; +``` + +### Warm-up exercise: Define a model type to average predictions + +Let's define a composite model type `MyAverageTwo` that +averages the predictions of two deterministic regressors. Here's the learning network: + +```julia:ex3 +X = source() +y = source(kind=:target) + +model1 = linear +model2 = knn + +m1 = machine(model1, X, y) +y1 = predict(m1, X) + +m2 = machine(model2, X, y) +y2 = predict(m2, X) + +yhat = 0.5*y1 + 0.5*y2 +``` + +And the macro call to define `MyAverageTwo` and an instance `average_two`: + +```julia:ex4 +avg = @from_network MyAverageTwo(regressor1=model1, + regressor2=model2) <= yhat +``` + +Evaluating this average model on the Boston data set, and comparing +with the base model predictions: + +```julia:ex5 +function print_performance(model, data...) + e = evaluate(model, data...; + resampling=CV(rng=1234, nfolds=8), + measure=rms, + verbosity=0) + μ = round(e.measurement[1], sigdigits=5) + ste = round(std(e.per_fold[1])/sqrt(8), digits=5) + println("\n $model = $μ ± $(2*ste)") +end; + +X, y = @load_boston + +print_performance(linear, X, y) +print_performance(knn, X, y) +print_performance(avg, X, y) +``` + +## Stacking proper +### Helper functions: + +To generate folds for generating out-of-sample predictions, we define + +```julia:ex6 +folds(data, nfolds) = + partition(1:nrows(data), (1/nfolds for i in 1:(nfolds-1))...); +``` + +For example, we have: + +```julia:ex7 +f = folds(1:10, 3) +``` + +In our learning network, the folds will depend on the input data, +which will be wrapped as a source node. We therefore need to +overload the `folds` function for nodes: + +```julia:ex8 +folds(X::AbstractNode, nfolds) = node(XX -> folds(XX, nfolds), X); +``` + +It will also be convenient to use the MLJ method `restrict(X, f, i)` +that restricts data `X` to the `i`th element (fold) of `f`, and +`corestrict(X, f, i)` that restricts to the corresponding fold +complement (the concatenation of all but the `i`th +fold). + +For example, we have: + +```julia:ex9 +corestrict(string.(1:10), f, 2) +``` + +Overloading these functions for nodes: + +```julia:ex10 +MLJ.restrict(X::AbstractNode, f::AbstractNode, i) = + node((XX, ff) -> restrict(XX, ff, i), X, f); +MLJ.corestrict(X::AbstractNode, f::AbstractNode, i) = + node((XX, ff) -> corestrict(XX, ff, i), X, f); +``` + +All the other data manipulations we will need (`vcat`, `hcat`, +`MLJ.table`) are already overloaded to work with nodes. + +### Choose some test data (optional) and some component models (defaults for the composite model): + +```julia:ex11 +figure(figsize=(8,6)) +steps(x) = x < -3/2 ? -1 : (x < 3/2 ? 0 : 1) +x = Float64[-4, -1, 2, -3, 0, 3, -2, 1, 4] +Xraw = (x = x, ) +yraw = steps.(x); +idxsort = sortperm(x) +xsort = x[idxsort] +ysort = yraw[idxsort] +step(xsort, ysort, label="truth", where="mid") +plot(x, yraw, ls="none", marker="o", label="data") +xlim(-4.5, 4.5) +legend() + +savefig(joinpath(@OUTPUT, "s1.svg")) # hide +``` + +\fig{s1.svg} + +Some models to stack: + +```julia:ex12 +model1 = linear +model2 = knn +``` + +The adjudicating model: + +```julia:ex13 +judge = linear +``` + +### Define the training nodes + +Let's instantiate some input and target source nodes for the +learning network, wrapping the play data defined above: + +Wrapped as source node: + +```julia:ex14 +X = source(Xraw) +y = source(yraw; kind=:target) +``` + +Our first internal node represents the three folds (vectors of row +indices) for creating the out-of-sample predictions: + +```julia:ex15 +f = folds(X, 3) +f() +``` + +Constructing machines for training `model1` on each fold-complement: + +```julia:ex16 +m11 = machine(model1, corestrict(X, f, 1), corestrict(y, f, 1)) +m12 = machine(model1, corestrict(X, f, 2), corestrict(y, f, 2)) +m13 = machine(model1, corestrict(X, f, 3), corestrict(y, f, 3)) +``` + +Define each out-of-sample prediction of `model1`: + +```julia:ex17 +y11 = predict(m11, restrict(X, f, 1)); +y12 = predict(m12, restrict(X, f, 2)); +y13 = predict(m13, restrict(X, f, 3)); +``` + +Splice together the out-of-sample predictions for model1: + +```julia:ex18 +y1_oos = vcat(y11, y12, y13); +``` + +Optionally, to check our network so far, we can fit and plot +`y1_oos`: + +```julia:ex19 +fit!(y1_oos, verbosity=0) + +figure(figsize=(8,6)) +step(xsort, ysort, label="truth", where="mid") +plot(x, y1_oos(), ls="none", marker="o", label="linear oos") + +savefig(joinpath(@OUTPUT, "s2.svg")) # hide +``` + +\fig{s2.svg} + +We now repeat the procedure for the other model: + +```julia:ex20 +m21 = machine(model2, corestrict(X, f, 1), corestrict(y, f, 1)) +m22 = machine(model2, corestrict(X, f, 2), corestrict(y, f, 2)) +m23 = machine(model2, corestrict(X, f, 3), corestrict(y, f, 3)) +y21 = predict(m21, restrict(X, f, 1)); +y22 = predict(m22, restrict(X, f, 2)); +y23 = predict(m23, restrict(X, f, 3)); +``` + +And testing the knn out-of-sample prediction: + +```julia:ex21 +y2_oos = vcat(y21, y22, y23); +fit!(y2_oos, verbosity=0) + +figure(figsize=(8,6)) +step(xsort, ysort, label="truth", where="mid") +plot(x, y2_oos(), ls="none", marker="o", label="knn oos") + +savefig(joinpath(@OUTPUT, "s3.svg")) # hide +``` + +\fig{s3.svg} + +Now that we have the out-of-sample base learner predictions, we are +ready to merge them into the adjudicator's input table and construct +the machine for training the adjudicator: + +```julia:ex22 +X_oos = MLJ.table(hcat(y1_oos, y2_oos)) +m_judge = machine(judge, X_oos, y) +``` + +Are we done with constructing machines? Well, not quite. Recall that +when use the stack to make predictions on new data, we will be +feeding the adjudicator ordinary predictions on the base +learners. But so far, we have only defined machines to train the +base learners on fold complements, not on the full data, which we do +now: + +```julia:ex23 +m1 = machine(model1, X, y) +m2 = machine(model2, X, y) +``` + +### Define nodes still needed for prediction + +To obtain the final prediction, `yhat`, we get the base learner +predictions, based on training with all data, and feed them to the +adjudicator: + +```julia:ex24 +y1 = predict(m1, X); +y2 = predict(m2, X); +X_judge = MLJ.table(hcat(y1, y2)) +yhat = predict(m_judge, X_judge) +``` + +Let's check the final prediction node can be fit and called: + +```julia:ex25 +fit!(yhat, verbosity=0) + +figure(figsize=(8,6)) +step(xsort, ysort, label="truth", where="mid") +plot(x, yhat(), ls="none", marker="o", label="yhat") + +savefig(joinpath(@OUTPUT, "s4.svg")) # hide +``` + +\fig{s4} + +Although of little statistical significance here, we note that +stacking gives a lower *training* error than naive averaging: + +```julia:ex26 +e1 = rms(y1(), y()) +e2 = rms(y2(), y()) +emean = rms(0.5*y1() + 0.5*y2(), y()) +estack = rms(yhat(), y()) +@show e1 e2 emean estack; +``` + +## Export the learning network as a new model type + +The learning network (less the data wrapped in the source nodes) +amounts to a specification of a new composite model type for +two-model stacks, trained with three-fold resampling of base model +predictions. Let's create the new type `MyTwoModelStack`: + +```julia:ex27 +@from_network MyTwoModelStack(regressor1=model1, + regressor2=model2, + judge=judge) <= yhat +``` + +And this completes the definition of our re-usable stacking model type. + +## Applying `MyTwoModelStack` to Ames House Price data + +Without undertaking any hyperparameter optimization, we evaluate the +performance of a random forest and ridge regressor on the well-known +Ames House Prices data, and compare the performance with a stack +(and simple averaging) using the random forest and ridge regressors +as base learners. We then indicate some options for tuning the +stack. + +#### Data pre-processing + +Here we use a 12-feature reduced subset of the Ames House Price data +set: + +```julia:ex28 +X0, y0 = @load_reduced_ames; +``` + +Inspect scitypes: + +```julia:ex29 +s = schema(X0) +(names=collect(s.names), scitypes=collect(s.scitypes)) |> pretty +``` + +Coerce counts and ordered factors to continuous: + +```julia:ex30 +X1 = coerce(X0, :OverallQual => Continuous, + :GarageCars => Continuous, + :YearRemodAdd => Continuous, + :YearBuilt => Continuous); +``` + +One-hot encode the multiclass: + +```julia:ex31 +hot_mach = fit!(machine(OneHotEncoder(), X1), verbosity=0) +X = transform(hot_mach, X1); +``` + +Check the final scitype: + +```julia:ex32 +scitype(X) +``` + +transform the target: + +```julia:ex33 +y1 = log.(y0) +y = transform(fit!(machine(UnivariateStandardizer(), y1), + verbosity=0), y1); +``` + +#### Define the stack and compare performance: + +```julia:ex34 +avg = MyAverageTwo(regressor1=forest, + regressor2=ridge) + + +stack = MyTwoModelStack(regressor1=forest, + regressor2=ridge, + judge=linear) + +all_models = [forest, ridge, avg, stack]; + +for model in all_models + print_performance(model, X, y) +end; +``` + +#### Tuning a stack + +A standard abuse of good data hygiene practice is to optimize stack +component models *separately* and then tune the adjudicating model +hyperparameters (using the same resampling of the data) with the +base learners fixed. Although more computationally expensive, better +generalization might be expected by applying tuning to the stack as +a whole, either simultaneously, or in in cheaper sequential +steps. Since our stack is a stand-alone model, this is readily +implemented. + +As a proof of concept, let's see how to tune one of the base model +hyperparameters, based on performance of the stack as a whole: + +```julia:ex35 +r = range(stack, :(regressor2.lambda), lower = 1, upper = 20, scale=:log) +tuned_stack = TunedModel(model=stack, + ranges=r, + tuning=Grid(), + measure=rms, + resampling=Holdout()) + +mach = fit!(machine(tuned_stack, X, y), verbosity=0) +best_stack = fitted_params(mach).best_model +best_stack.regressor2.lambda +``` + +Let's evaluate the best stack using the same data resampling used to +the evaluate the assorted untuned models earlier (now we are neglecting +data hygeine!): + +```julia:ex36 +print_performance(best_stack, X, y) + +PyPlot.close_figs() # hide +``` + diff --git a/__site/assets/literate/A-stacking_script.jl b/__site/assets/literate/A-stacking_script.jl new file mode 100644 index 00000000..a25a0060 --- /dev/null +++ b/__site/assets/literate/A-stacking_script.jl @@ -0,0 +1,198 @@ +# This file was generated, do not modify it. + +using MLJ, PyPlot +MLJ.color_off() # hide +import Random.seed! +seed!(1234) + +linear = @load LinearRegressor pkg=MLJLinearModels +ridge = @load RidgeRegressor pkg=MultivariateStats; ridge.lambda = 0.01 +knn = @load KNNRegressor; knn.K = 4 +tree = @load DecisionTreeRegressor; min_samples_leaf=1 +forest = @load RandomForestRegressor pkg=DecisionTree; forest.n_trees=500 +svm = @load SVMRegressor; + +X = source() +y = source(kind=:target) + +model1 = linear +model2 = knn + +m1 = machine(model1, X, y) +y1 = predict(m1, X) + +m2 = machine(model2, X, y) +y2 = predict(m2, X) + +yhat = 0.5*y1 + 0.5*y2 + +avg = @from_network MyAverageTwo(regressor1=model1, + regressor2=model2) <= yhat + +function print_performance(model, data...) + e = evaluate(model, data...; + resampling=CV(rng=1234, nfolds=8), + measure=rms, + verbosity=0) + μ = round(e.measurement[1], sigdigits=5) + ste = round(std(e.per_fold[1])/sqrt(8), digits=5) + println("\n $model = $μ ± $(2*ste)") +end; + +X, y = @load_boston + +print_performance(linear, X, y) +print_performance(knn, X, y) +print_performance(avg, X, y) + +folds(data, nfolds) = + partition(1:nrows(data), (1/nfolds for i in 1:(nfolds-1))...); + +f = folds(1:10, 3) + +folds(X::AbstractNode, nfolds) = node(XX -> folds(XX, nfolds), X); + +corestrict(string.(1:10), f, 2) + +MLJ.restrict(X::AbstractNode, f::AbstractNode, i) = + node((XX, ff) -> restrict(XX, ff, i), X, f); +MLJ.corestrict(X::AbstractNode, f::AbstractNode, i) = + node((XX, ff) -> corestrict(XX, ff, i), X, f); + +figure(figsize=(8,6)) +steps(x) = x < -3/2 ? -1 : (x < 3/2 ? 0 : 1) +x = Float64[-4, -1, 2, -3, 0, 3, -2, 1, 4] +Xraw = (x = x, ) +yraw = steps.(x); +idxsort = sortperm(x) +xsort = x[idxsort] +ysort = yraw[idxsort] +step(xsort, ysort, label="truth", where="mid") +plot(x, yraw, ls="none", marker="o", label="data") +xlim(-4.5, 4.5) +legend() + +savefig(joinpath(@OUTPUT, "s1.svg")) # hide + +model1 = linear +model2 = knn + +judge = linear + +X = source(Xraw) +y = source(yraw; kind=:target) + +f = folds(X, 3) +f() + +m11 = machine(model1, corestrict(X, f, 1), corestrict(y, f, 1)) +m12 = machine(model1, corestrict(X, f, 2), corestrict(y, f, 2)) +m13 = machine(model1, corestrict(X, f, 3), corestrict(y, f, 3)) + +y11 = predict(m11, restrict(X, f, 1)); +y12 = predict(m12, restrict(X, f, 2)); +y13 = predict(m13, restrict(X, f, 3)); + +y1_oos = vcat(y11, y12, y13); + +fit!(y1_oos, verbosity=0) + +figure(figsize=(8,6)) +step(xsort, ysort, label="truth", where="mid") +plot(x, y1_oos(), ls="none", marker="o", label="linear oos") + +savefig(joinpath(@OUTPUT, "s2.svg")) # hide + +m21 = machine(model2, corestrict(X, f, 1), corestrict(y, f, 1)) +m22 = machine(model2, corestrict(X, f, 2), corestrict(y, f, 2)) +m23 = machine(model2, corestrict(X, f, 3), corestrict(y, f, 3)) +y21 = predict(m21, restrict(X, f, 1)); +y22 = predict(m22, restrict(X, f, 2)); +y23 = predict(m23, restrict(X, f, 3)); + +y2_oos = vcat(y21, y22, y23); +fit!(y2_oos, verbosity=0) + +figure(figsize=(8,6)) +step(xsort, ysort, label="truth", where="mid") +plot(x, y2_oos(), ls="none", marker="o", label="knn oos") + +savefig(joinpath(@OUTPUT, "s3.svg")) # hide + +X_oos = MLJ.table(hcat(y1_oos, y2_oos)) +m_judge = machine(judge, X_oos, y) + +m1 = machine(model1, X, y) +m2 = machine(model2, X, y) + +y1 = predict(m1, X); +y2 = predict(m2, X); +X_judge = MLJ.table(hcat(y1, y2)) +yhat = predict(m_judge, X_judge) + +fit!(yhat, verbosity=0) + +figure(figsize=(8,6)) +step(xsort, ysort, label="truth", where="mid") +plot(x, yhat(), ls="none", marker="o", label="yhat") + +savefig(joinpath(@OUTPUT, "s4.svg")) # hide + +e1 = rms(y1(), y()) +e2 = rms(y2(), y()) +emean = rms(0.5*y1() + 0.5*y2(), y()) +estack = rms(yhat(), y()) +@show e1 e2 emean estack; + +@from_network MyTwoModelStack(regressor1=model1, + regressor2=model2, + judge=judge) <= yhat + +X0, y0 = @load_reduced_ames; + +s = schema(X0) +(names=collect(s.names), scitypes=collect(s.scitypes)) |> pretty + +X1 = coerce(X0, :OverallQual => Continuous, + :GarageCars => Continuous, + :YearRemodAdd => Continuous, + :YearBuilt => Continuous); + +hot_mach = fit!(machine(OneHotEncoder(), X1), verbosity=0) +X = transform(hot_mach, X1); + +scitype(X) + +y1 = log.(y0) +y = transform(fit!(machine(UnivariateStandardizer(), y1), + verbosity=0), y1); + +avg = MyAverageTwo(regressor1=forest, + regressor2=ridge) + + +stack = MyTwoModelStack(regressor1=forest, + regressor2=ridge, + judge=linear) + +all_models = [forest, ridge, avg, stack]; + +for model in all_models + print_performance(model, X, y) +end; + +r = range(stack, :(regressor2.lambda), lower = 1, upper = 20, scale=:log) +tuned_stack = TunedModel(model=stack, + ranges=r, + tuning=Grid(), + measure=rms, + resampling=Holdout()) + +mach = fit!(machine(tuned_stack, X, y), verbosity=0) +best_stack = fitted_params(mach).best_model +best_stack.regressor2.lambda + +print_performance(best_stack, X, y) + +PyPlot.close_figs() # hide + diff --git a/__site/data/categorical/index.html b/__site/data/categorical/index.html index d752cf5b..5fb37ab6 100644 --- a/__site/data/categorical/index.html +++ b/__site/data/categorical/index.html @@ -1,4 +1,4 @@ - Handling categorical data

Handling categorical data

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save). This tutorial follows loosely the docs.

Defining a categorical vector

using CategoricalArrays
+         Handling categorical data    

Handling categorical data

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save). This tutorial follows loosely the docs.

Defining a categorical vector

using CategoricalArrays
 
 v = categorical(["AA", "BB", "CC", "AA", "BB", "CC"])
6-element CategoricalArrays.CategoricalArray{String,1,UInt32}:
  "AA"
diff --git a/__site/data/dataframe/index.html b/__site/data/dataframe/index.html
index b6eddc2d..4e15d83b 100644
--- a/__site/data/dataframe/index.html
+++ b/__site/data/dataframe/index.html
@@ -1,4 +1,4 @@
-         Manipulating a DataFrame    

Manipulating a DataFrame

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save). This tutorial is loosely adapted from this pandas tutorial as well as the DataFrames.jl documentation. It is by no means meant to be a complete introduction, rather, it focuses on some key functionalities that are particularly useful in a classical machine learning context.

Basics

To start with, we will use the Boston dataset which is very simple.

using RDatasets, DataFrames
+         Manipulating a DataFrame    

Manipulating a DataFrame

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save). This tutorial is loosely adapted from this pandas tutorial as well as the DataFrames.jl documentation. It is by no means meant to be a complete introduction, rather, it focuses on some key functionalities that are particularly useful in a classical machine learning context.

Basics

To start with, we will use the Boston dataset which is very simple.

using RDatasets, DataFrames
 
 boston = dataset("MASS", "Boston");

The dataset function returns a DataFrame object:

typeof(boston)
DataFrames.DataFrame

Accessing data

diff --git a/__site/data/loading/index.html b/__site/data/loading/index.html index ae6765e9..14facbae 100644 --- a/__site/data/loading/index.html +++ b/__site/data/loading/index.html @@ -1,4 +1,4 @@ - Loading and elementary processing of data

Loading and elementary processing of data

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save). In this short tutorial we discuss two ways to easily load data in Julia:

  1. loading a standard dataset via RDatasets.jl,

  2. loading a local file with CSV.jl,

Using RDatasets

The package RDatasets.jl provides access to most of the many datasets listed on this page. These are well known, standard datasets that can be used to get started with data processing and classical machine learning such as for instance iris, crabs, Boston, etc.

To load such a dataset, you will need to specify which R package it belongs to as well as its name; for instance Boston is part of MASS.

using RDatasets
+         Loading and elementary processing of data    

Loading and elementary processing of data

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save). In this short tutorial we discuss two ways to easily load data in Julia:

  1. loading a standard dataset via RDatasets.jl,

  2. loading a local file with CSV.jl,

Using RDatasets

The package RDatasets.jl provides access to most of the many datasets listed on this page. These are well known, standard datasets that can be used to get started with data processing and classical machine learning such as for instance iris, crabs, Boston, etc.

To load such a dataset, you will need to specify which R package it belongs to as well as its name; for instance Boston is part of MASS.

using RDatasets
 
 boston = dataset("MASS", "Boston");

The fact that Boston is part of MASS is clearly indicated on the list linked to earlier. While it can be a bit slow, loading a dataset via RDatasets is very simple and convenient as you don't have to worry about setting the names of columns etc.

The dataset function returns a DataFrame object from the DataFrames.jl package.

typeof(boston)
DataFrames.DataFrame

For a short introduction to DataFrame objects, see this tutorial.

diff --git a/__site/data/scitype/index.html b/__site/data/scitype/index.html index c322ed89..a43c145a 100644 --- a/__site/data/scitype/index.html +++ b/__site/data/scitype/index.html @@ -1,4 +1,4 @@ - Data interpretation: Scientific Types

Data interpretation: Scientific Types

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Machine type vs Scientific Type

Why make a distinction?

When analysing data, it is important to distinguish between

  • how the data is encoded (e.g. Int), and

  • how the data should be interpreted (e.g. a class label, a count, ...)

How the data is encoded will be referred to as the machine type whereas how the data should be interpreted will be referred to as the scientific type (or scitype).

In some cases, this may be un-ambiguous, for instance if you have a vector of floating point values, this should usually be interpreted as a continuous feature (e.g.: weights, speeds, temperatures, ...).

In many other cases however, there may be ambiguities, we list a few examples below:

  • A vector of Int e.g. [1, 2, ...] which should be interpreted as categorical labels,

  • A vector of Int e.g. [1, 2, ...] which should be interpreted as count data,

  • A vector of String e.g. ["High", "Low", "High", ...] which should be interpreted as ordered categorical labels,

  • A vector of String e.g. ["John", "Maria", ...] which should not interpreted as informative data,

  • A vector of floating points [1.5, 1.5, -2.3, -2.3] which should be interpreted as categorical data (e.g. the few possible values of some setting), etc.

The Scientific Types

The package ScientificTypes.jl defines a barebone type hierarchy which can be used to indicate how a particular feature should be interpreted; in particular:

Found
+         Data interpretation: Scientific Types    

Data interpretation: Scientific Types

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Machine type vs Scientific Type

Why make a distinction?

When analysing data, it is important to distinguish between

  • how the data is encoded (e.g. Int), and

  • how the data should be interpreted (e.g. a class label, a count, ...)

How the data is encoded will be referred to as the machine type whereas how the data should be interpreted will be referred to as the scientific type (or scitype).

In some cases, this may be un-ambiguous, for instance if you have a vector of floating point values, this should usually be interpreted as a continuous feature (e.g.: weights, speeds, temperatures, ...).

In many other cases however, there may be ambiguities, we list a few examples below:

  • A vector of Int e.g. [1, 2, ...] which should be interpreted as categorical labels,

  • A vector of Int e.g. [1, 2, ...] which should be interpreted as count data,

  • A vector of String e.g. ["High", "Low", "High", ...] which should be interpreted as ordered categorical labels,

  • A vector of String e.g. ["John", "Maria", ...] which should not interpreted as informative data,

  • A vector of floating points [1.5, 1.5, -2.3, -2.3] which should be interpreted as categorical data (e.g. the few possible values of some setting), etc.

The Scientific Types

The package ScientificTypes.jl defines a barebone type hierarchy which can be used to indicate how a particular feature should be interpreted; in particular:

Found
 ├─ Known
 │  ├─ Textual
 │  ├─ Finite
diff --git a/__site/e1.svg b/__site/e1.svg
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diff --git a/__site/e2.svg b/__site/e2.svg
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diff --git a/__site/end-to-end/AMES/index.html b/__site/end-to-end/AMES/index.html
index 06426500..1d6835dc 100644
--- a/__site/end-to-end/AMES/index.html
+++ b/__site/end-to-end/AMES/index.html
@@ -1,4 +1,4 @@
-         AMES    

AMES

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Baby steps

Let's load a reduced version of the well-known Ames House Price data set (containing six of the more important categorical features and six of the more important numerical features). As "iris" the dataset is so common that you can load it directly with @load_ames and the reduced version via @load_reduced_ames

using MLJ, PrettyPrinting, DataFrames, Statistics
+         AMES    

AMES

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Baby steps

Let's load a reduced version of the well-known Ames House Price data set (containing six of the more important categorical features and six of the more important numerical features). As "iris" the dataset is so common that you can load it directly with @load_ames and the reduced version via @load_reduced_ames

using MLJ, PrettyPrinting, DataFrames, Statistics
 
 X, y = @load_reduced_ames
 X = DataFrame(X)
diff --git a/__site/end-to-end/crabs-xgb/index.html b/__site/end-to-end/crabs-xgb/index.html
index 1783c22a..c176b786 100644
--- a/__site/end-to-end/crabs-xgb/index.html
+++ b/__site/end-to-end/crabs-xgb/index.html
@@ -1,4 +1,4 @@
-         Crabs with XGBoost    

Crabs with XGBoost

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save). This example is inspired from this post showing how to use XGBoost.

First steps

Again, the crabs dataset is so common that there is a simple load function for it:

using MLJ, StatsBase, Random, PyPlot, CategoricalArrays
+         Crabs with XGBoost    

Crabs with XGBoost

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save). This example is inspired from this post showing how to use XGBoost.

First steps

Again, the crabs dataset is so common that there is a simple load function for it:

using MLJ, StatsBase, Random, PyPlot, CategoricalArrays
 using PrettyPrinting, DataFrames, LossFunctions
 X, y = @load_crabs
 X = DataFrame(X)
diff --git a/__site/end-to-end/horse/index.html b/__site/end-to-end/horse/index.html
index 4889af31..e553a18c 100644
--- a/__site/end-to-end/horse/index.html
+++ b/__site/end-to-end/horse/index.html
@@ -1,4 +1,4 @@
-         Horse colic data    

Horse colic data

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Initial data processing

In this example, we consider the UCI "horse colic" dataset

This is a reasonably messy classification problem with missing values etc and so some work should be expected in the feature processing.

Getting the data

The data is pre-split in training and testing and we will keep it as such

using MLJ, StatsBase
+         Horse colic data    

Horse colic data

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Initial data processing

In this example, we consider the UCI "horse colic" dataset

This is a reasonably messy classification problem with missing values etc and so some work should be expected in the feature processing.

Getting the data

The data is pre-split in training and testing and we will keep it as such

using MLJ, StatsBase
 using HTTP, CSV, DataFrames
 req1 = HTTP.get("https://archive.ics.uci.edu/ml/machine-learning-databases/horse-colic/horse-colic.data")
 req2 = HTTP.get("https://archive.ics.uci.edu/ml/machine-learning-databases/horse-colic/horse-colic.test")
diff --git a/__site/end-to-end/wine/index.html b/__site/end-to-end/wine/index.html
index 19738c6b..406d2e35 100644
--- a/__site/end-to-end/wine/index.html
+++ b/__site/end-to-end/wine/index.html
@@ -1,4 +1,4 @@
-         Wine    

Wine

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Initial data processing

In this example, we consider the UCI "wine" dataset

These data are the results of a chemical analysis of wines grown in the same region in Italy but derived from three different cultivars. The analysis determined the quantities of 13 constituents found in each of the three types of wines.

Getting the data

Let's download the data thanks to the HTTP.jl package and load it into a DataFrame via the CSV.jl package:

using HTTP, CSV, MLJ, StatsBase, PyPlot
+         Wine    

Wine

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Initial data processing

In this example, we consider the UCI "wine" dataset

These data are the results of a chemical analysis of wines grown in the same region in Italy but derived from three different cultivars. The analysis determined the quantities of 13 constituents found in each of the three types of wines.

Getting the data

Let's download the data thanks to the HTTP.jl package and load it into a DataFrame via the CSV.jl package:

using HTTP, CSV, MLJ, StatsBase, PyPlot
 req = HTTP.get("https://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data")
 data = CSV.read(req.body,
                 header=["Class", "Alcool", "Malic acid",
diff --git a/__site/generated/notebooks/A-ensembles-3.ipynb b/__site/generated/notebooks/A-ensembles-3.ipynb
new file mode 100644
index 00000000..3d7cc805
--- /dev/null
+++ b/__site/generated/notebooks/A-ensembles-3.ipynb
@@ -0,0 +1,258 @@
+{
+ "cells": [
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Before running this, please make sure to activate and instantiate the environment\n",
+    "corresponding to [this `Project.toml`](https://raw.githubusercontent.com/alan-turing-institute/MLJTutorials/master/Project.toml) and [this `Manifest.toml`](https://raw.githubusercontent.com/alan-turing-institute/MLJTutorials/master/Manifest.toml)\n",
+    "so that you get an environment which matches the one used to generate the tutorials:\n",
+    "\n",
+    "```julia\n",
+    "cd(\"MLJTutorials\") # cd to folder with the *.toml\n",
+    "using Pkg; Pkg.activate(\".\"); Pkg.instantiate()\n",
+    "```"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "# Simple example of a homogeneous ensemble using learning networks"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "In this simple example, no bagging is used, so every atomic model\n",
+    "gets the same learned parameters, unless the atomic model training\n",
+    "algorithm has randomness, eg, DecisionTree with random subsampling\n",
+    "of features at nodes."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Note that MLJ has a built in model wrapper called `EnsembleModel`\n",
+    "for creating bagged ensembles with a few lines of code."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "## Definition of composite model type"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "using MLJ, PyPlot\n",
+    "import Statistics"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "learning network (composite model spec):"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "Xs = source()\n",
+    "ys = source(kind=:target)\n",
+    "\n",
+    "atom = @load DecisionTreeRegressor\n",
+    "atom.n_subfeatures = 4 # to ensure diversity among trained atomic models\n",
+    "\n",
+    "machines = (machine(atom, Xs, ys) for i in 1:100)"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "overload `mean` for nodes:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "Statistics.mean(v...) = mean(v)\n",
+    "Statistics.mean(v::AbstractVector{<:AbstractNode}) = node(mean, v...)\n",
+    "\n",
+    "yhat = mean([predict(m, Xs) for  m in machines]);"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "new composite model type and instance:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "one_hundred_models = @from_network OneHundredModels(atom=atom) <= yhat"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "## Application to data"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "X, y = @load_boston;"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "tune regularization parameter for a *single* tree:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "r = range(atom,\n",
+    "          :min_samples_split,\n",
+    "          lower=2,\n",
+    "          upper=100, scale=:log)\n",
+    "\n",
+    "mach = machine(atom, X, y)\n",
+    "\n",
+    "curve = learning_curve!(mach,\n",
+    "                        range=r,\n",
+    "                        measure=mav,\n",
+    "                        resampling=CV(nfolds=9),\n",
+    "                        verbosity=0)\n",
+    "\n",
+    "plot(curve.parameter_values, curve.measurements)\n",
+    "xlabel(curve.parameter_name)\n",
+    "\n",
+    "savefig(joinpath(@OUTPUT, \"e1.svg\")) # hide"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "\\fig{e1.svg}"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "tune regularization parameter for all trees in ensemble simultaneously:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "r = range(one_hundred_models,\n",
+    "          :(atom.min_samples_split),\n",
+    "          lower=2,\n",
+    "          upper=100, scale=:log)\n",
+    "\n",
+    "mach = machine(one_hundred_models, X, y)\n",
+    "\n",
+    "curve = learning_curve!(mach,\n",
+    "                        range=r,\n",
+    "                        measure=mav,\n",
+    "                        resampling=CV(nfolds=9),\n",
+    "                        verbosity=0)\n",
+    "\n",
+    "plot(curve.parameter_values, curve.measurements)\n",
+    "xlabel(curve.parameter_name)\n",
+    "\n",
+    "savefig(joinpath(@OUTPUT, \"e2.svg\")) # hide"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "\\fig{e2}"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "PyPlot.close_figs() # hide"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "---\n",
+    "\n",
+    "*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*"
+   ],
+   "metadata": {}
+  }
+ ],
+ "nbformat_minor": 3,
+ "metadata": {
+  "language_info": {
+   "file_extension": ".jl",
+   "mimetype": "application/julia",
+   "name": "julia",
+   "version": "1.5.0-DEV.145"
+  },
+  "kernelspec": {
+   "name": "julia-1.5",
+   "display_name": "Julia 1.5.0-DEV.145",
+   "language": "julia"
+  }
+ },
+ "nbformat": 4
+}
diff --git a/__site/generated/notebooks/A-stacking.ipynb b/__site/generated/notebooks/A-stacking.ipynb
new file mode 100644
index 00000000..5bc9687d
--- /dev/null
+++ b/__site/generated/notebooks/A-stacking.ipynb
@@ -0,0 +1,1082 @@
+{
+ "cells": [
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Before running this, please make sure to activate and instantiate the environment\n",
+    "corresponding to [this `Project.toml`](https://raw.githubusercontent.com/alan-turing-institute/MLJTutorials/master/Project.toml) and [this `Manifest.toml`](https://raw.githubusercontent.com/alan-turing-institute/MLJTutorials/master/Manifest.toml)\n",
+    "so that you get an environment which matches the one used to generate the tutorials:\n",
+    "\n",
+    "```julia\n",
+    "cd(\"MLJTutorials\") # cd to folder with the *.toml\n",
+    "using Pkg; Pkg.activate(\".\"); Pkg.instantiate()\n",
+    "```"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "In stacking one blends the predictions of different regressors or\n",
+    "classifiers to gain, in some cases, better performance than naive\n",
+    "averaging or majority vote."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Here we illustrate how to build a two-model stack as an MLJ learning\n",
+    "network, which we export as a new stand-alone composite model\n",
+    "type `MyTwoStack`. This will make the stack that we build completely\n",
+    "re-usable (new data, new models) and means we can apply\n",
+    "meta-algorithms, such as performance evaluation and tuning, to the\n",
+    "stack, exaclty as we would for any other model."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Our main purpose here is to demonstrate the flexibility of MLJ's\n",
+    "composite model interface. Eventually, MLJ will provide built-in\n",
+    "composite types or macros to achieve the same results in a few\n",
+    "lines, which will suffice for routine stacking tasks."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "After defining the `MyTwoStack` model type, we instantiate it for an\n",
+    "application to the Ames House Price data set."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "## Basic stacking using out-of-sample base learner predictions"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "A rather general stacking protocol was first described in a [1992\n",
+    "paper](https://www.sciencedirect.com/science/article/abs/pii/S0893608005800231)\n",
+    "by David Wolpert. For a generic introduction to the basic two-layer\n",
+    "stack described here, see [this blog\n",
+    "post](https://burakhimmetoglu.com/2016/12/01/stacking-models-for-improved-predictions/)\n",
+    "of Burak Himmetoglu."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "A basic stack consists of a number of base learners (two, in this\n",
+    "illustration) and a single adjudicating model."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "When a stacked model is called to make a prediction, the individual\n",
+    "predictions of the base learners are made the columns of an *input*\n",
+    "table for the adjudicating model, which then outputs the final\n",
+    "prediction. However, it is crucial to understand that the flow of\n",
+    "data *during training* is not the same."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "The base model predictions used to train the adjudicating model are\n",
+    "*not* the predictions of the base learners fitted to all the\n",
+    "training data. Rather, to prevent the adjudicator giving too much\n",
+    "weight to the base learners with low *training* error, the input\n",
+    "data is first split into a number of folds (as in cross-validation),\n",
+    "a base learner is trained on each fold complement individually, and\n",
+    "corresponding predictions on the folds are spliced together to form\n",
+    "a full-length prediction called the *out-of-sample.prediction*."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "For illustrative purposes we use just three folds. Each base learner\n",
+    "will get three separate machines, for training on each fold\n",
+    "complement, and a fourth machine, trained on all the supplied data,\n",
+    "for use in the prediction flow."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "We build the learning network with dummy data at the source nodes,\n",
+    "so the reader inspect the workings of the network as it is built (by\n",
+    "calling `fit!` on nodes, and by calling the nodes themselves). As\n",
+    "usual, this data is not seen by the exported composite model type,\n",
+    "and the component models we choose are just default values for the\n",
+    "hyperparameters of the composite model."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "using MLJ, PyPlot\n",
+    "MLJ.color_off() # hide\n",
+    "import Random.seed!\n",
+    "seed!(1234)"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Some models we will use:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "linear = @load LinearRegressor pkg=MLJLinearModels\n",
+    "ridge = @load RidgeRegressor pkg=MultivariateStats; ridge.lambda = 0.01\n",
+    "knn = @load KNNRegressor; knn.K = 4\n",
+    "tree = @load DecisionTreeRegressor; min_samples_leaf=1\n",
+    "forest = @load RandomForestRegressor pkg=DecisionTree; forest.n_trees=500\n",
+    "svm = @load SVMRegressor;"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "### Warm-up exercise: Define a model type to average predictions"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Let's define a composite model type `MyAverageTwo` that\n",
+    "averages the predictions of two deterministic regressors. Here's the learning network:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "X = source()\n",
+    "y = source(kind=:target)\n",
+    "\n",
+    "model1 = linear\n",
+    "model2 = knn\n",
+    "\n",
+    "m1 = machine(model1, X, y)\n",
+    "y1 = predict(m1, X)\n",
+    "\n",
+    "m2 = machine(model2, X, y)\n",
+    "y2 = predict(m2, X)\n",
+    "\n",
+    "yhat = 0.5*y1 + 0.5*y2"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "And the macro call to define `MyAverageTwo` and an instance `average_two`:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "avg = @from_network MyAverageTwo(regressor1=model1,\n",
+    "                                 regressor2=model2) <= yhat"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Evaluating this average model on the Boston data set, and comparing\n",
+    "with the base model predictions:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "function print_performance(model, data...)\n",
+    "    e = evaluate(model, data...;\n",
+    "                 resampling=CV(rng=1234, nfolds=8),\n",
+    "                 measure=rms,\n",
+    "                 verbosity=0)\n",
+    "    μ = round(e.measurement[1], sigdigits=5)\n",
+    "    ste = round(std(e.per_fold[1])/sqrt(8), digits=5)\n",
+    "    println(\"\\n $model = $μ ± $(2*ste)\")\n",
+    "end;\n",
+    "\n",
+    "X, y = @load_boston\n",
+    "\n",
+    "print_performance(linear, X, y)\n",
+    "print_performance(knn, X, y)\n",
+    "print_performance(avg, X, y)"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "## Stacking proper\n",
+    "### Helper functions:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "To generate folds for generating out-of-sample predictions, we define"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "folds(data, nfolds) =\n",
+    "    partition(1:nrows(data), (1/nfolds for i in 1:(nfolds-1))...);"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "For example, we have:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "f = folds(1:10, 3)"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "In our learning network, the folds will depend on the input data,\n",
+    "which will be wrapped as a source node. We therefore need to\n",
+    "overload the `folds` function for nodes:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "folds(X::AbstractNode, nfolds) = node(XX -> folds(XX, nfolds), X);"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "It will also be convenient to use the MLJ method `restrict(X, f, i)`\n",
+    "that restricts data `X` to the `i`th element (fold) of `f`, and\n",
+    "`corestrict(X, f, i)` that restricts to the corresponding fold\n",
+    "complement (the concatenation of all but the `i`th\n",
+    "fold)."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "For example, we have:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "corestrict(string.(1:10), f, 2)"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Overloading these functions for nodes:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "MLJ.restrict(X::AbstractNode, f::AbstractNode, i) =\n",
+    "    node((XX, ff) -> restrict(XX, ff, i), X, f);\n",
+    "MLJ.corestrict(X::AbstractNode, f::AbstractNode, i) =\n",
+    "    node((XX, ff) -> corestrict(XX, ff, i), X, f);"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "All the other data manipulations we will need (`vcat`, `hcat`,\n",
+    "`MLJ.table`) are already overloaded to work with nodes."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "### Choose some test data (optional) and some component models (defaults for the composite model):"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "figure(figsize=(8,6))\n",
+    "steps(x) = x < -3/2 ? -1 : (x < 3/2 ? 0 : 1)\n",
+    "x = Float64[-4, -1, 2, -3, 0, 3, -2, 1, 4]\n",
+    "Xraw = (x = x, )\n",
+    "yraw = steps.(x);\n",
+    "idxsort = sortperm(x)\n",
+    "xsort = x[idxsort]\n",
+    "ysort = yraw[idxsort]\n",
+    "step(xsort, ysort, label=\"truth\", where=\"mid\")\n",
+    "plot(x, yraw, ls=\"none\", marker=\"o\", label=\"data\")\n",
+    "xlim(-4.5, 4.5)\n",
+    "legend()\n",
+    "\n",
+    "savefig(joinpath(@OUTPUT, \"s1.svg\")) # hide"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "\\fig{s1.svg}"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Some models to stack:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "model1 = linear\n",
+    "model2 = knn"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "The adjudicating model:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "judge = linear"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "### Define the training nodes"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Let's instantiate some input and target source nodes for the\n",
+    "learning network, wrapping the play data defined above:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Wrapped as source node:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "X = source(Xraw)\n",
+    "y = source(yraw; kind=:target)"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Our first internal node represents the three folds (vectors of row\n",
+    "indices) for creating the out-of-sample predictions:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "f = folds(X, 3)\n",
+    "f()"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Constructing machines for training `model1` on each fold-complement:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "m11 = machine(model1, corestrict(X, f, 1), corestrict(y, f, 1))\n",
+    "m12 = machine(model1, corestrict(X, f, 2), corestrict(y, f, 2))\n",
+    "m13 = machine(model1, corestrict(X, f, 3), corestrict(y, f, 3))"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Define each out-of-sample prediction of `model1`:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "y11 = predict(m11, restrict(X, f, 1));\n",
+    "y12 = predict(m12, restrict(X, f, 2));\n",
+    "y13 = predict(m13, restrict(X, f, 3));"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Splice together the out-of-sample predictions for model1:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "y1_oos = vcat(y11, y12, y13);"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Optionally, to check our network so far, we can fit and plot\n",
+    "`y1_oos`:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "fit!(y1_oos, verbosity=0)\n",
+    "\n",
+    "figure(figsize=(8,6))\n",
+    "step(xsort, ysort, label=\"truth\", where=\"mid\")\n",
+    "plot(x, y1_oos(), ls=\"none\", marker=\"o\", label=\"linear oos\")\n",
+    "\n",
+    "savefig(joinpath(@OUTPUT, \"s2.svg\")) # hide"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "\\fig{s2.svg}"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "We now repeat the procedure for the other model:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "m21 = machine(model2, corestrict(X, f, 1), corestrict(y, f, 1))\n",
+    "m22 = machine(model2, corestrict(X, f, 2), corestrict(y, f, 2))\n",
+    "m23 = machine(model2, corestrict(X, f, 3), corestrict(y, f, 3))\n",
+    "y21 = predict(m21, restrict(X, f, 1));\n",
+    "y22 = predict(m22, restrict(X, f, 2));\n",
+    "y23 = predict(m23, restrict(X, f, 3));"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "And testing the knn out-of-sample prediction:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "y2_oos = vcat(y21, y22, y23);\n",
+    "fit!(y2_oos, verbosity=0)\n",
+    "\n",
+    "figure(figsize=(8,6))\n",
+    "step(xsort, ysort, label=\"truth\", where=\"mid\")\n",
+    "plot(x, y2_oos(), ls=\"none\", marker=\"o\", label=\"knn oos\")\n",
+    "\n",
+    "savefig(joinpath(@OUTPUT, \"s3.svg\")) # hide"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "\\fig{s3.svg}"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Now that we have the out-of-sample base learner predictions, we are\n",
+    "ready to merge them into the adjudicator's input table and construct\n",
+    "the machine for training the adjudicator:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "X_oos = MLJ.table(hcat(y1_oos, y2_oos))\n",
+    "m_judge = machine(judge, X_oos, y)"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Are we done with constructing machines? Well, not quite. Recall that\n",
+    "when use the stack to make predictions on new data, we will be\n",
+    "feeding the adjudicator ordinary predictions on the base\n",
+    "learners. But so far, we have only defined machines to train the\n",
+    "base learners on fold complements, not on the full data, which we do\n",
+    "now:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "m1 = machine(model1, X, y)\n",
+    "m2 = machine(model2, X, y)"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "### Define nodes still needed for prediction"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "To obtain the final prediction, `yhat`, we get the base learner\n",
+    "predictions, based on training with all data, and feed them to the\n",
+    "adjudicator:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "y1 = predict(m1, X);\n",
+    "y2 = predict(m2, X);\n",
+    "X_judge = MLJ.table(hcat(y1, y2))\n",
+    "yhat = predict(m_judge, X_judge)"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Let's check the final prediction node can be fit and called:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "fit!(yhat, verbosity=0)\n",
+    "\n",
+    "figure(figsize=(8,6))\n",
+    "step(xsort, ysort, label=\"truth\", where=\"mid\")\n",
+    "plot(x, yhat(), ls=\"none\", marker=\"o\", label=\"yhat\")\n",
+    "\n",
+    "savefig(joinpath(@OUTPUT, \"s4.svg\")) # hide"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "\\fig{s4}"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Although of little statistical significance here, we note that\n",
+    "stacking gives a lower *training* error than naive averaging:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "e1 = rms(y1(), y())\n",
+    "e2 = rms(y2(), y())\n",
+    "emean = rms(0.5*y1() + 0.5*y2(), y())\n",
+    "estack = rms(yhat(), y())\n",
+    "@show e1 e2 emean estack;"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "## Export the learning network as a new model type"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "The learning network (less the data wrapped in the source nodes)\n",
+    "amounts to a specification of a new composite model type for\n",
+    "two-model stacks, trained with three-fold resampling of base model\n",
+    "predictions. Let's create the new type `MyTwoModelStack`:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "@from_network MyTwoModelStack(regressor1=model1,\n",
+    "                              regressor2=model2,\n",
+    "                              judge=judge) <= yhat"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "And this completes the definition of our re-usable stacking model type."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "## Applying `MyTwoModelStack` to Ames House Price data"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Without undertaking any hyperparameter optimization, we evaluate the\n",
+    "performance of a random forest and ridge regressor on the well-known\n",
+    "Ames House Prices data, and compare the performance with a stack\n",
+    "(and simple averaging) using the random forest and ridge regressors\n",
+    "as base learners. We then indicate some options for tuning the\n",
+    "stack."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "#### Data pre-processing"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Here we use a 12-feature reduced subset of the Ames House Price data\n",
+    "set:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "X0, y0 = @load_reduced_ames;"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Inspect scitypes:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "s = schema(X0)\n",
+    "(names=collect(s.names), scitypes=collect(s.scitypes)) |> pretty"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Coerce counts and ordered factors to continuous:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "X1 = coerce(X0, :OverallQual => Continuous,\n",
+    "            :GarageCars => Continuous,\n",
+    "            :YearRemodAdd => Continuous,\n",
+    "            :YearBuilt => Continuous);"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "One-hot encode the multiclass:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "hot_mach = fit!(machine(OneHotEncoder(), X1), verbosity=0)\n",
+    "X = transform(hot_mach, X1);"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Check the final scitype:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "scitype(X)"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "transform the target:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "y1 = log.(y0)\n",
+    "y = transform(fit!(machine(UnivariateStandardizer(), y1),\n",
+    "                   verbosity=0), y1);"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "#### Define the stack and compare performance:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "avg = MyAverageTwo(regressor1=forest,\n",
+    "                   regressor2=ridge)\n",
+    "\n",
+    "\n",
+    "stack = MyTwoModelStack(regressor1=forest,\n",
+    "                        regressor2=ridge,\n",
+    "                        judge=linear)\n",
+    "\n",
+    "all_models = [forest, ridge, avg, stack];\n",
+    "\n",
+    "for model in all_models\n",
+    "    print_performance(model, X, y)\n",
+    "end;"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "#### Tuning a stack"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "A standard abuse of good data hygiene practice is to optimize stack\n",
+    "component models *separately* and then tune the adjudicating model\n",
+    "hyperparameters (using the same resampling of the data) with the\n",
+    "base learners fixed. Although more computationally expensive, better\n",
+    "generalization might be expected by applying tuning to the stack as\n",
+    "a whole, either simultaneously, or in in cheaper sequential\n",
+    "steps. Since our stack is a stand-alone model, this is readily\n",
+    "implemented."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "As a proof of concept, let's see how to tune one of the base model\n",
+    "hyperparameters, based on performance of the stack as a whole:"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "r = range(stack, :(regressor2.lambda), lower = 1, upper = 20, scale=:log)\n",
+    "tuned_stack = TunedModel(model=stack,\n",
+    "                         ranges=r,\n",
+    "                         tuning=Grid(),\n",
+    "                         measure=rms,\n",
+    "                         resampling=Holdout())\n",
+    "\n",
+    "mach = fit!(machine(tuned_stack,  X, y), verbosity=0)\n",
+    "best_stack = fitted_params(mach).best_model\n",
+    "best_stack.regressor2.lambda"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "Let's evaluate the best stack using the same data resampling used to\n",
+    "the evaluate the assorted untuned models earlier (now we are neglecting\n",
+    "data hygeine!):"
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "print_performance(best_stack, X, y)\n",
+    "\n",
+    "PyPlot.close_figs() # hide"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "outputs": [],
+   "cell_type": "markdown",
+   "source": [
+    "---\n",
+    "\n",
+    "*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*"
+   ],
+   "metadata": {}
+  }
+ ],
+ "nbformat_minor": 3,
+ "metadata": {
+  "language_info": {
+   "file_extension": ".jl",
+   "mimetype": "application/julia",
+   "name": "julia",
+   "version": "1.5.0-DEV.145"
+  },
+  "kernelspec": {
+   "name": "julia-1.5",
+   "display_name": "Julia 1.5.0-DEV.145",
+   "language": "julia"
+  }
+ },
+ "nbformat": 4
+}
diff --git a/__site/generated/scripts/A-ensembles-3-raw.jl b/__site/generated/scripts/A-ensembles-3-raw.jl
new file mode 100644
index 00000000..b32b7acc
--- /dev/null
+++ b/__site/generated/scripts/A-ensembles-3-raw.jl
@@ -0,0 +1,69 @@
+# Before running this, please make sure to activate and instantiate the environment
+# corresponding to [this `Project.toml`](https://raw.githubusercontent.com/alan-turing-institute/MLJTutorials/master/Project.toml) and [this `Manifest.toml`](https://raw.githubusercontent.com/alan-turing-institute/MLJTutorials/master/Manifest.toml)
+# so that you get an environment which matches the one used to generate the tutorials:
+#
+# ```julia
+# cd("MLJTutorials") # cd to folder with the *.toml
+# using Pkg; Pkg.activate("."); Pkg.instantiate()
+# ```
+
+using MLJ, PyPlot
+import Statistics
+
+Xs = source()
+ys = source(kind=:target)
+
+atom = @load DecisionTreeRegressor
+atom.n_subfeatures = 4 # to ensure diversity among trained atomic models
+
+machines = (machine(atom, Xs, ys) for i in 1:100)
+
+Statistics.mean(v...) = mean(v)
+Statistics.mean(v::AbstractVector{<:AbstractNode}) = node(mean, v...)
+
+yhat = mean([predict(m, Xs) for  m in machines]);
+
+one_hundred_models = @from_network OneHundredModels(atom=atom) <= yhat
+
+X, y = @load_boston;
+
+r = range(atom,
+          :min_samples_split,
+          lower=2,
+          upper=100, scale=:log)
+
+mach = machine(atom, X, y)
+
+curve = learning_curve!(mach,
+                        range=r,
+                        measure=mav,
+                        resampling=CV(nfolds=9),
+                        verbosity=0)
+
+plot(curve.parameter_values, curve.measurements)
+xlabel(curve.parameter_name)
+
+
+
+r = range(one_hundred_models,
+          :(atom.min_samples_split),
+          lower=2,
+          upper=100, scale=:log)
+
+mach = machine(one_hundred_models, X, y)
+
+curve = learning_curve!(mach,
+                        range=r,
+                        measure=mav,
+                        resampling=CV(nfolds=9),
+                        verbosity=0)
+
+plot(curve.parameter_values, curve.measurements)
+xlabel(curve.parameter_name)
+
+
+
+
+
+# This file was generated using Literate.jl, https://github.com/fredrikekre/Literate.jl
+
diff --git a/__site/generated/scripts/A-ensembles-3.jl b/__site/generated/scripts/A-ensembles-3.jl
new file mode 100644
index 00000000..cd5abe43
--- /dev/null
+++ b/__site/generated/scripts/A-ensembles-3.jl
@@ -0,0 +1,81 @@
+# Before running this, please make sure to activate and instantiate the environment
+# corresponding to [this `Project.toml`](https://raw.githubusercontent.com/alan-turing-institute/MLJTutorials/master/Project.toml) and [this `Manifest.toml`](https://raw.githubusercontent.com/alan-turing-institute/MLJTutorials/master/Manifest.toml)
+# so that you get an environment which matches the one used to generate the tutorials:
+#
+# ```julia
+# cd("MLJTutorials") # cd to folder with the *.toml
+# using Pkg; Pkg.activate("."); Pkg.instantiate()
+# ```
+
+# # Simple example of a homogeneous ensemble using learning networks
+# In this simple example, no bagging is used, so every atomic model# gets the same learned parameters, unless the atomic model training# algorithm has randomness, eg, DecisionTree with random subsampling# of features at nodes.
+# Note that MLJ has a built in model wrapper called `EnsembleModel`# for creating bagged ensembles with a few lines of code.
+# ## Definition of composite model type
+using MLJ, PyPlot
+import Statistics
+
+# learning network (composite model spec):
+Xs = source()
+ys = source(kind=:target)
+
+atom = @load DecisionTreeRegressor
+atom.n_subfeatures = 4 # to ensure diversity among trained atomic models
+
+machines = (machine(atom, Xs, ys) for i in 1:100)
+
+# overload `mean` for nodes:
+Statistics.mean(v...) = mean(v)
+Statistics.mean(v::AbstractVector{<:AbstractNode}) = node(mean, v...)
+
+yhat = mean([predict(m, Xs) for  m in machines]);
+
+# new composite model type and instance:
+one_hundred_models = @from_network OneHundredModels(atom=atom) <= yhat
+
+# ## Application to data
+X, y = @load_boston;
+
+# tune regularization parameter for a *single* tree:
+r = range(atom,
+          :min_samples_split,
+          lower=2,
+          upper=100, scale=:log)
+
+mach = machine(atom, X, y)
+
+curve = learning_curve!(mach,
+                        range=r,
+                        measure=mav,
+                        resampling=CV(nfolds=9),
+                        verbosity=0)
+
+plot(curve.parameter_values, curve.measurements)
+xlabel(curve.parameter_name)
+
+
+
+# \fig{e1.svg}
+# tune regularization parameter for all trees in ensemble simultaneously:
+r = range(one_hundred_models,
+          :(atom.min_samples_split),
+          lower=2,
+          upper=100, scale=:log)
+
+mach = machine(one_hundred_models, X, y)
+
+curve = learning_curve!(mach,
+                        range=r,
+                        measure=mav,
+                        resampling=CV(nfolds=9),
+                        verbosity=0)
+
+plot(curve.parameter_values, curve.measurements)
+xlabel(curve.parameter_name)
+
+
+
+# \fig{e2}
+
+
+# This file was generated using Literate.jl, https://github.com/fredrikekre/Literate.jl
+
diff --git a/__site/generated/scripts/A-stacking-raw.jl b/__site/generated/scripts/A-stacking-raw.jl
new file mode 100644
index 00000000..1727c752
--- /dev/null
+++ b/__site/generated/scripts/A-stacking-raw.jl
@@ -0,0 +1,207 @@
+# Before running this, please make sure to activate and instantiate the environment
+# corresponding to [this `Project.toml`](https://raw.githubusercontent.com/alan-turing-institute/MLJTutorials/master/Project.toml) and [this `Manifest.toml`](https://raw.githubusercontent.com/alan-turing-institute/MLJTutorials/master/Manifest.toml)
+# so that you get an environment which matches the one used to generate the tutorials:
+#
+# ```julia
+# cd("MLJTutorials") # cd to folder with the *.toml
+# using Pkg; Pkg.activate("."); Pkg.instantiate()
+# ```
+
+using MLJ, PyPlot
+
+import Random.seed!
+seed!(1234)
+
+linear = @load LinearRegressor pkg=MLJLinearModels
+ridge = @load RidgeRegressor pkg=MultivariateStats; ridge.lambda = 0.01
+knn = @load KNNRegressor; knn.K = 4
+tree = @load DecisionTreeRegressor; min_samples_leaf=1
+forest = @load RandomForestRegressor pkg=DecisionTree; forest.n_trees=500
+svm = @load SVMRegressor;
+
+X = source()
+y = source(kind=:target)
+
+model1 = linear
+model2 = knn
+
+m1 = machine(model1, X, y)
+y1 = predict(m1, X)
+
+m2 = machine(model2, X, y)
+y2 = predict(m2, X)
+
+yhat = 0.5*y1 + 0.5*y2
+
+avg = @from_network MyAverageTwo(regressor1=model1,
+                                 regressor2=model2) <= yhat
+
+function print_performance(model, data...)
+    e = evaluate(model, data...;
+                 resampling=CV(rng=1234, nfolds=8),
+                 measure=rms,
+                 verbosity=0)
+    μ = round(e.measurement[1], sigdigits=5)
+    ste = round(std(e.per_fold[1])/sqrt(8), digits=5)
+    println("\n $model = $μ ± $(2*ste)")
+end;
+
+X, y = @load_boston
+
+print_performance(linear, X, y)
+print_performance(knn, X, y)
+print_performance(avg, X, y)
+
+folds(data, nfolds) =
+    partition(1:nrows(data), (1/nfolds for i in 1:(nfolds-1))...);
+
+f = folds(1:10, 3)
+
+folds(X::AbstractNode, nfolds) = node(XX -> folds(XX, nfolds), X);
+
+corestrict(string.(1:10), f, 2)
+
+MLJ.restrict(X::AbstractNode, f::AbstractNode, i) =
+    node((XX, ff) -> restrict(XX, ff, i), X, f);
+MLJ.corestrict(X::AbstractNode, f::AbstractNode, i) =
+    node((XX, ff) -> corestrict(XX, ff, i), X, f);
+
+figure(figsize=(8,6))
+steps(x) = x < -3/2 ? -1 : (x < 3/2 ? 0 : 1)
+x = Float64[-4, -1, 2, -3, 0, 3, -2, 1, 4]
+Xraw = (x = x, )
+yraw = steps.(x);
+idxsort = sortperm(x)
+xsort = x[idxsort]
+ysort = yraw[idxsort]
+step(xsort, ysort, label="truth", where="mid")
+plot(x, yraw, ls="none", marker="o", label="data")
+xlim(-4.5, 4.5)
+legend()
+
+
+
+model1 = linear
+model2 = knn
+
+judge = linear
+
+X = source(Xraw)
+y = source(yraw; kind=:target)
+
+f = folds(X, 3)
+f()
+
+m11 = machine(model1, corestrict(X, f, 1), corestrict(y, f, 1))
+m12 = machine(model1, corestrict(X, f, 2), corestrict(y, f, 2))
+m13 = machine(model1, corestrict(X, f, 3), corestrict(y, f, 3))
+
+y11 = predict(m11, restrict(X, f, 1));
+y12 = predict(m12, restrict(X, f, 2));
+y13 = predict(m13, restrict(X, f, 3));
+
+y1_oos = vcat(y11, y12, y13);
+
+fit!(y1_oos, verbosity=0)
+
+figure(figsize=(8,6))
+step(xsort, ysort, label="truth", where="mid")
+plot(x, y1_oos(), ls="none", marker="o", label="linear oos")
+
+
+
+m21 = machine(model2, corestrict(X, f, 1), corestrict(y, f, 1))
+m22 = machine(model2, corestrict(X, f, 2), corestrict(y, f, 2))
+m23 = machine(model2, corestrict(X, f, 3), corestrict(y, f, 3))
+y21 = predict(m21, restrict(X, f, 1));
+y22 = predict(m22, restrict(X, f, 2));
+y23 = predict(m23, restrict(X, f, 3));
+
+y2_oos = vcat(y21, y22, y23);
+fit!(y2_oos, verbosity=0)
+
+figure(figsize=(8,6))
+step(xsort, ysort, label="truth", where="mid")
+plot(x, y2_oos(), ls="none", marker="o", label="knn oos")
+
+
+
+X_oos = MLJ.table(hcat(y1_oos, y2_oos))
+m_judge = machine(judge, X_oos, y)
+
+m1 = machine(model1, X, y)
+m2 = machine(model2, X, y)
+
+y1 = predict(m1, X);
+y2 = predict(m2, X);
+X_judge = MLJ.table(hcat(y1, y2))
+yhat = predict(m_judge, X_judge)
+
+fit!(yhat, verbosity=0)
+
+figure(figsize=(8,6))
+step(xsort, ysort, label="truth", where="mid")
+plot(x, yhat(), ls="none", marker="o", label="yhat")
+
+
+
+e1 = rms(y1(), y())
+e2 = rms(y2(), y())
+emean = rms(0.5*y1() + 0.5*y2(), y())
+estack = rms(yhat(), y())
+@show e1 e2 emean estack;
+
+@from_network MyTwoModelStack(regressor1=model1,
+                              regressor2=model2,
+                              judge=judge) <= yhat
+
+X0, y0 = @load_reduced_ames;
+
+s = schema(X0)
+(names=collect(s.names), scitypes=collect(s.scitypes)) |> pretty
+
+X1 = coerce(X0, :OverallQual => Continuous,
+            :GarageCars => Continuous,
+            :YearRemodAdd => Continuous,
+            :YearBuilt => Continuous);
+
+hot_mach = fit!(machine(OneHotEncoder(), X1), verbosity=0)
+X = transform(hot_mach, X1);
+
+scitype(X)
+
+y1 = log.(y0)
+y = transform(fit!(machine(UnivariateStandardizer(), y1),
+                   verbosity=0), y1);
+
+avg = MyAverageTwo(regressor1=forest,
+                   regressor2=ridge)
+
+
+stack = MyTwoModelStack(regressor1=forest,
+                        regressor2=ridge,
+                        judge=linear)
+
+all_models = [forest, ridge, avg, stack];
+
+for model in all_models
+    print_performance(model, X, y)
+end;
+
+r = range(stack, :(regressor2.lambda), lower = 1, upper = 20, scale=:log)
+tuned_stack = TunedModel(model=stack,
+                         ranges=r,
+                         tuning=Grid(),
+                         measure=rms,
+                         resampling=Holdout())
+
+mach = fit!(machine(tuned_stack,  X, y), verbosity=0)
+best_stack = fitted_params(mach).best_model
+best_stack.regressor2.lambda
+
+print_performance(best_stack, X, y)
+
+
+
+# This file was generated using Literate.jl, https://github.com/fredrikekre/Literate.jl
+
diff --git a/__site/generated/scripts/A-stacking.jl b/__site/generated/scripts/A-stacking.jl
new file mode 100644
index 00000000..ecd7d434
--- /dev/null
+++ b/__site/generated/scripts/A-stacking.jl
@@ -0,0 +1,271 @@
+# Before running this, please make sure to activate and instantiate the environment
+# corresponding to [this `Project.toml`](https://raw.githubusercontent.com/alan-turing-institute/MLJTutorials/master/Project.toml) and [this `Manifest.toml`](https://raw.githubusercontent.com/alan-turing-institute/MLJTutorials/master/Manifest.toml)
+# so that you get an environment which matches the one used to generate the tutorials:
+#
+# ```julia
+# cd("MLJTutorials") # cd to folder with the *.toml
+# using Pkg; Pkg.activate("."); Pkg.instantiate()
+# ```
+
+# In stacking one blends the predictions of different regressors or# classifiers to gain, in some cases, better performance than naive# averaging or majority vote.
+# Here we illustrate how to build a two-model stack as an MLJ learning# network, which we export as a new stand-alone composite model# type `MyTwoStack`. This will make the stack that we build completely# re-usable (new data, new models) and means we can apply# meta-algorithms, such as performance evaluation and tuning, to the# stack, exaclty as we would for any other model.
+# Our main purpose here is to demonstrate the flexibility of MLJ's# composite model interface. Eventually, MLJ will provide built-in# composite types or macros to achieve the same results in a few# lines, which will suffice for routine stacking tasks.
+# After defining the `MyTwoStack` model type, we instantiate it for an# application to the Ames House Price data set.
+# ## Basic stacking using out-of-sample base learner predictions
+# A rather general stacking protocol was first described in a [1992# paper](https://www.sciencedirect.com/science/article/abs/pii/S0893608005800231)# by David Wolpert. For a generic introduction to the basic two-layer# stack described here, see [this blog# post](https://burakhimmetoglu.com/2016/12/01/stacking-models-for-improved-predictions/)# of Burak Himmetoglu.
+# A basic stack consists of a number of base learners (two, in this# illustration) and a single adjudicating model.
+# When a stacked model is called to make a prediction, the individual# predictions of the base learners are made the columns of an *input*# table for the adjudicating model, which then outputs the final# prediction. However, it is crucial to understand that the flow of# data *during training* is not the same.
+# The base model predictions used to train the adjudicating model are# *not* the predictions of the base learners fitted to all the# training data. Rather, to prevent the adjudicator giving too much# weight to the base learners with low *training* error, the input# data is first split into a number of folds (as in cross-validation),# a base learner is trained on each fold complement individually, and# corresponding predictions on the folds are spliced together to form# a full-length prediction called the *out-of-sample.prediction*.
+# For illustrative purposes we use just three folds. Each base learner# will get three separate machines, for training on each fold# complement, and a fourth machine, trained on all the supplied data,# for use in the prediction flow.
+# We build the learning network with dummy data at the source nodes,# so the reader inspect the workings of the network as it is built (by# calling `fit!` on nodes, and by calling the nodes themselves). As# usual, this data is not seen by the exported composite model type,# and the component models we choose are just default values for the# hyperparameters of the composite model.
+using MLJ, PyPlot
+
+import Random.seed!
+seed!(1234)
+
+# Some models we will use:
+linear = @load LinearRegressor pkg=MLJLinearModels
+ridge = @load RidgeRegressor pkg=MultivariateStats; ridge.lambda = 0.01
+knn = @load KNNRegressor; knn.K = 4
+tree = @load DecisionTreeRegressor; min_samples_leaf=1
+forest = @load RandomForestRegressor pkg=DecisionTree; forest.n_trees=500
+svm = @load SVMRegressor;
+
+# ### Warm-up exercise: Define a model type to average predictions
+# Let's define a composite model type `MyAverageTwo` that# averages the predictions of two deterministic regressors. Here's the learning network:
+X = source()
+y = source(kind=:target)
+
+model1 = linear
+model2 = knn
+
+m1 = machine(model1, X, y)
+y1 = predict(m1, X)
+
+m2 = machine(model2, X, y)
+y2 = predict(m2, X)
+
+yhat = 0.5*y1 + 0.5*y2
+
+# And the macro call to define `MyAverageTwo` and an instance `average_two`:
+avg = @from_network MyAverageTwo(regressor1=model1,
+                                 regressor2=model2) <= yhat
+
+# Evaluating this average model on the Boston data set, and comparing# with the base model predictions:
+function print_performance(model, data...)
+    e = evaluate(model, data...;
+                 resampling=CV(rng=1234, nfolds=8),
+                 measure=rms,
+                 verbosity=0)
+    μ = round(e.measurement[1], sigdigits=5)
+    ste = round(std(e.per_fold[1])/sqrt(8), digits=5)
+    println("\n $model = $μ ± $(2*ste)")
+end;
+
+X, y = @load_boston
+
+print_performance(linear, X, y)
+print_performance(knn, X, y)
+print_performance(avg, X, y)
+
+# ## Stacking proper# ### Helper functions:
+# To generate folds for generating out-of-sample predictions, we define
+folds(data, nfolds) =
+    partition(1:nrows(data), (1/nfolds for i in 1:(nfolds-1))...);
+
+# For example, we have:
+f = folds(1:10, 3)
+
+# In our learning network, the folds will depend on the input data,# which will be wrapped as a source node. We therefore need to# overload the `folds` function for nodes:
+folds(X::AbstractNode, nfolds) = node(XX -> folds(XX, nfolds), X);
+
+# It will also be convenient to use the MLJ method `restrict(X, f, i)`# that restricts data `X` to the `i`th element (fold) of `f`, and# `corestrict(X, f, i)` that restricts to the corresponding fold# complement (the concatenation of all but the `i`th# fold).
+# For example, we have:
+corestrict(string.(1:10), f, 2)
+
+# Overloading these functions for nodes:
+MLJ.restrict(X::AbstractNode, f::AbstractNode, i) =
+    node((XX, ff) -> restrict(XX, ff, i), X, f);
+MLJ.corestrict(X::AbstractNode, f::AbstractNode, i) =
+    node((XX, ff) -> corestrict(XX, ff, i), X, f);
+
+# All the other data manipulations we will need (`vcat`, `hcat`,# `MLJ.table`) are already overloaded to work with nodes.
+# ### Choose some test data (optional) and some component models (defaults for the composite model):
+figure(figsize=(8,6))
+steps(x) = x < -3/2 ? -1 : (x < 3/2 ? 0 : 1)
+x = Float64[-4, -1, 2, -3, 0, 3, -2, 1, 4]
+Xraw = (x = x, )
+yraw = steps.(x);
+idxsort = sortperm(x)
+xsort = x[idxsort]
+ysort = yraw[idxsort]
+step(xsort, ysort, label="truth", where="mid")
+plot(x, yraw, ls="none", marker="o", label="data")
+xlim(-4.5, 4.5)
+legend()
+
+
+
+# \fig{s1.svg}
+# Some models to stack:
+model1 = linear
+model2 = knn
+
+# The adjudicating model:
+judge = linear
+
+# ### Define the training nodes
+# Let's instantiate some input and target source nodes for the# learning network, wrapping the play data defined above:
+# Wrapped as source node:
+X = source(Xraw)
+y = source(yraw; kind=:target)
+
+# Our first internal node represents the three folds (vectors of row# indices) for creating the out-of-sample predictions:
+f = folds(X, 3)
+f()
+
+# Constructing machines for training `model1` on each fold-complement:
+m11 = machine(model1, corestrict(X, f, 1), corestrict(y, f, 1))
+m12 = machine(model1, corestrict(X, f, 2), corestrict(y, f, 2))
+m13 = machine(model1, corestrict(X, f, 3), corestrict(y, f, 3))
+
+# Define each out-of-sample prediction of `model1`:
+y11 = predict(m11, restrict(X, f, 1));
+y12 = predict(m12, restrict(X, f, 2));
+y13 = predict(m13, restrict(X, f, 3));
+
+# Splice together the out-of-sample predictions for model1:
+y1_oos = vcat(y11, y12, y13);
+
+# Optionally, to check our network so far, we can fit and plot# `y1_oos`:
+fit!(y1_oos, verbosity=0)
+
+figure(figsize=(8,6))
+step(xsort, ysort, label="truth", where="mid")
+plot(x, y1_oos(), ls="none", marker="o", label="linear oos")
+
+
+
+# \fig{s2.svg}
+# We now repeat the procedure for the other model:
+m21 = machine(model2, corestrict(X, f, 1), corestrict(y, f, 1))
+m22 = machine(model2, corestrict(X, f, 2), corestrict(y, f, 2))
+m23 = machine(model2, corestrict(X, f, 3), corestrict(y, f, 3))
+y21 = predict(m21, restrict(X, f, 1));
+y22 = predict(m22, restrict(X, f, 2));
+y23 = predict(m23, restrict(X, f, 3));
+
+# And testing the knn out-of-sample prediction:
+y2_oos = vcat(y21, y22, y23);
+fit!(y2_oos, verbosity=0)
+
+figure(figsize=(8,6))
+step(xsort, ysort, label="truth", where="mid")
+plot(x, y2_oos(), ls="none", marker="o", label="knn oos")
+
+
+
+# \fig{s3.svg}
+# Now that we have the out-of-sample base learner predictions, we are# ready to merge them into the adjudicator's input table and construct# the machine for training the adjudicator:
+X_oos = MLJ.table(hcat(y1_oos, y2_oos))
+m_judge = machine(judge, X_oos, y)
+
+# Are we done with constructing machines? Well, not quite. Recall that# when use the stack to make predictions on new data, we will be# feeding the adjudicator ordinary predictions on the base# learners. But so far, we have only defined machines to train the# base learners on fold complements, not on the full data, which we do# now:
+m1 = machine(model1, X, y)
+m2 = machine(model2, X, y)
+
+# ### Define nodes still needed for prediction
+# To obtain the final prediction, `yhat`, we get the base learner# predictions, based on training with all data, and feed them to the# adjudicator:
+y1 = predict(m1, X);
+y2 = predict(m2, X);
+X_judge = MLJ.table(hcat(y1, y2))
+yhat = predict(m_judge, X_judge)
+
+# Let's check the final prediction node can be fit and called:
+fit!(yhat, verbosity=0)
+
+figure(figsize=(8,6))
+step(xsort, ysort, label="truth", where="mid")
+plot(x, yhat(), ls="none", marker="o", label="yhat")
+
+
+
+# \fig{s4}
+# Although of little statistical significance here, we note that# stacking gives a lower *training* error than naive averaging:
+e1 = rms(y1(), y())
+e2 = rms(y2(), y())
+emean = rms(0.5*y1() + 0.5*y2(), y())
+estack = rms(yhat(), y())
+@show e1 e2 emean estack;
+
+# ## Export the learning network as a new model type
+# The learning network (less the data wrapped in the source nodes)# amounts to a specification of a new composite model type for# two-model stacks, trained with three-fold resampling of base model# predictions. Let's create the new type `MyTwoModelStack`:
+@from_network MyTwoModelStack(regressor1=model1,
+                              regressor2=model2,
+                              judge=judge) <= yhat
+
+# And this completes the definition of our re-usable stacking model type.
+# ## Applying `MyTwoModelStack` to Ames House Price data
+# Without undertaking any hyperparameter optimization, we evaluate the# performance of a random forest and ridge regressor on the well-known# Ames House Prices data, and compare the performance with a stack# (and simple averaging) using the random forest and ridge regressors# as base learners. We then indicate some options for tuning the# stack.
+# #### Data pre-processing
+# Here we use a 12-feature reduced subset of the Ames House Price data# set:
+X0, y0 = @load_reduced_ames;
+
+# Inspect scitypes:
+s = schema(X0)
+(names=collect(s.names), scitypes=collect(s.scitypes)) |> pretty
+
+# Coerce counts and ordered factors to continuous:
+X1 = coerce(X0, :OverallQual => Continuous,
+            :GarageCars => Continuous,
+            :YearRemodAdd => Continuous,
+            :YearBuilt => Continuous);
+
+# One-hot encode the multiclass:
+hot_mach = fit!(machine(OneHotEncoder(), X1), verbosity=0)
+X = transform(hot_mach, X1);
+
+# Check the final scitype:
+scitype(X)
+
+# transform the target:
+y1 = log.(y0)
+y = transform(fit!(machine(UnivariateStandardizer(), y1),
+                   verbosity=0), y1);
+
+# #### Define the stack and compare performance:
+avg = MyAverageTwo(regressor1=forest,
+                   regressor2=ridge)
+
+
+stack = MyTwoModelStack(regressor1=forest,
+                        regressor2=ridge,
+                        judge=linear)
+
+all_models = [forest, ridge, avg, stack];
+
+for model in all_models
+    print_performance(model, X, y)
+end;
+
+# #### Tuning a stack
+# A standard abuse of good data hygiene practice is to optimize stack# component models *separately* and then tune the adjudicating model# hyperparameters (using the same resampling of the data) with the# base learners fixed. Although more computationally expensive, better# generalization might be expected by applying tuning to the stack as# a whole, either simultaneously, or in in cheaper sequential# steps. Since our stack is a stand-alone model, this is readily# implemented.
+# As a proof of concept, let's see how to tune one of the base model# hyperparameters, based on performance of the stack as a whole:
+r = range(stack, :(regressor2.lambda), lower = 1, upper = 20, scale=:log)
+tuned_stack = TunedModel(model=stack,
+                         ranges=r,
+                         tuning=Grid(),
+                         measure=rms,
+                         resampling=Holdout())
+
+mach = fit!(machine(tuned_stack,  X, y), verbosity=0)
+best_stack = fitted_params(mach).best_model
+best_stack.regressor2.lambda
+
+# Let's evaluate the best stack using the same data resampling used to# the evaluate the assorted untuned models earlier (now we are neglecting# data hygeine!):
+print_performance(best_stack, X, y)
+
+
+
+# This file was generated using Literate.jl, https://github.com/fredrikekre/Literate.jl
+
diff --git a/__site/getting-started/choosing-a-model/index.html b/__site/getting-started/choosing-a-model/index.html
index 7a501787..77042f0c 100644
--- a/__site/getting-started/choosing-a-model/index.html
+++ b/__site/getting-started/choosing-a-model/index.html
@@ -1,4 +1,4 @@
-         Choosing and evaluating a model    

Choosing and evaluating a model

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Data and its interpretation

Machine type and scientific type

using RDatasets, MLJ
+         Choosing and evaluating a model    

Choosing and evaluating a model

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Data and its interpretation

Machine type and scientific type

using RDatasets, MLJ
 iris = dataset("datasets", "iris")
 
 first(iris, 3) |> pretty
┌─────────────┬────────────┬─────────────┬────────────┬────────────────────────────────────────────┐
diff --git a/__site/getting-started/composing-models/index.html b/__site/getting-started/composing-models/index.html
index acc3a512..297ec8a0 100644
--- a/__site/getting-started/composing-models/index.html
+++ b/__site/getting-started/composing-models/index.html
@@ -1,4 +1,4 @@
-         Composing models    

Composing models

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Generating dummy data

Let's start by generating some dummy data with both numerical values and categorical values:

using MLJ, PrettyPrinting
+         Composing models    

Composing models

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Generating dummy data

Let's start by generating some dummy data with both numerical values and categorical values:

using MLJ, PrettyPrinting
 @load KNNRegressor
 # input
 X = (age    = [23, 45, 34, 25, 67],
diff --git a/__site/getting-started/ensembles-2/index.html b/__site/getting-started/ensembles-2/index.html
index accbaf9d..c3a7c0dd 100644
--- a/__site/getting-started/ensembles-2/index.html
+++ b/__site/getting-started/ensembles-2/index.html
@@ -1,4 +1,4 @@
-         Ensemble models (2)    

Ensemble models (2)

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Prelims

This tutorial builds upon the previous ensemble tutorial with a home-made Random Forest regressor on the "boston" dataset.

using MLJ, PyPlot, PrettyPrinting, Random,
+         Ensemble models (2)    

Ensemble models (2)

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Prelims

This tutorial builds upon the previous ensemble tutorial with a home-made Random Forest regressor on the "boston" dataset.

using MLJ, PyPlot, PrettyPrinting, Random,
       DataFrames
 X, y = @load_boston
 sch = schema(X)
diff --git a/__site/getting-started/ensembles-3/index.html b/__site/getting-started/ensembles-3/index.html
new file mode 100644
index 00000000..21e072cb
--- /dev/null
+++ b/__site/getting-started/ensembles-3/index.html
@@ -0,0 +1,71 @@
+         Ensemble models - extended tutorial    

Ensemble models - extended tutorial

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Simple example of a homogeneous ensemble using learning networks

In this simple example, no bagging is used, so every atomic model gets the same learned parameters, unless the atomic model training algorithm has randomness, eg, DecisionTree with random subsampling of features at nodes.

Note that MLJ has a built in model wrapper called EnsembleModel for creating bagged ensembles with a few lines of code.

Definition of composite model type

using MLJ, PyPlot
+import Statistics

learning network (composite model spec):

Xs = source()
+ys = source(kind=:target)
+
+atom = @load DecisionTreeRegressor
+atom.n_subfeatures = 4 # to ensure diversity among trained atomic models
+
+machines = (machine(atom, Xs, ys) for i in 1:100)
Base.Generator{UnitRange{Int64},Main.FD_SANDBOX_15866893453267974565.var"#1#2"}(Main.FD_SANDBOX_15866893453267974565.var"#1#2"(), 1:100)
+

overload mean for nodes:

+
Statistics.mean(v...) = mean(v)
+Statistics.mean(v::AbstractVector{<:AbstractNode}) = node(mean, v...)
+
+yhat = mean([predict(m, Xs) for  m in machines]);
+

new composite model type and instance:

+
one_hundred_models = @from_network OneHundredModels(atom=atom) <= yhat
OneHundredModels(
+    atom = DecisionTreeRegressor(
+            max_depth = -1,
+            min_samples_leaf = 5,
+            min_samples_split = 2,
+            min_purity_increase = 0.0,
+            n_subfeatures = 4,
+            post_prune = false,
+            merge_purity_threshold = 1.0)) @ 1…12
+

Application to data

+
X, y = @load_boston;
+

tune regularization parameter for a single tree:

+
r = range(atom,
+          :min_samples_split,
+          lower=2,
+          upper=100, scale=:log)
+
+mach = machine(atom, X, y)
+
+curve = learning_curve!(mach,
+                        range=r,
+                        measure=mav,
+                        resampling=CV(nfolds=9),
+                        verbosity=0)
+
+plot(curve.parameter_values, curve.measurements)
+xlabel(curve.parameter_name)
+ +

tune regularization parameter for all trees in ensemble simultaneously:

+
r = range(one_hundred_models,
+          :(atom.min_samples_split),
+          lower=2,
+          upper=100, scale=:log)
+
+mach = machine(one_hundred_models, X, y)
+
+curve = learning_curve!(mach,
+                        range=r,
+                        measure=mav,
+                        resampling=CV(nfolds=9),
+                        verbosity=0)
+
+plot(curve.parameter_values, curve.measurements)
+xlabel(curve.parameter_name)
+ + +
+ +
+ +
+ +
+
+ \ No newline at end of file diff --git a/__site/getting-started/ensembles/index.html b/__site/getting-started/ensembles/index.html index 372ea228..b56df0f6 100644 --- a/__site/getting-started/ensembles/index.html +++ b/__site/getting-started/ensembles/index.html @@ -1,4 +1,4 @@ - Ensemble models

Ensemble models

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Preliminary steps

Let's start by loading the relevant packages and generating some dummy data.

using MLJ, DataFrames, Statistics, PrettyPrinting
+         Ensemble models    

Ensemble models

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Preliminary steps

Let's start by loading the relevant packages and generating some dummy data.

using MLJ, DataFrames, Statistics, PrettyPrinting
 Xraw = rand(300, 3)
 y = exp.(Xraw[:,1] - Xraw[:,2] - 2Xraw[:,3] + 0.1*rand(300))
 X = DataFrame(Xraw)
diff --git a/__site/getting-started/fit-and-predict/index.html b/__site/getting-started/fit-and-predict/index.html
index 9a466880..a813159c 100644
--- a/__site/getting-started/fit-and-predict/index.html
+++ b/__site/getting-started/fit-and-predict/index.html
@@ -1,4 +1,4 @@
-         Fit, predict, transform    

Fit, predict, transform

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Preliminary steps

Data

As in "choosing a model", let's load the Iris dataset and unpack it:

using MLJ, Statistics, PrettyPrinting
+         Fit, predict, transform    

Fit, predict, transform

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Preliminary steps

Data

As in "choosing a model", let's load the Iris dataset and unpack it:

using MLJ, Statistics, PrettyPrinting
 X, y = @load_iris;

let's also load the DecisionTreeClassifier:

@load DecisionTreeClassifier
 tree_model = DecisionTreeClassifier()
DecisionTreeClassifier(
     max_depth = -1,
diff --git a/__site/getting-started/learning-networks-2/index.html b/__site/getting-started/learning-networks-2/index.html
index 40e3d542..0770f461 100644
--- a/__site/getting-started/learning-networks-2/index.html
+++ b/__site/getting-started/learning-networks-2/index.html
@@ -1,4 +1,4 @@
-         Learning networks 2    

Learning networks 2

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Preliminary steps

Let's start as with the previous tutorial:

using MLJ, DataFrames, Random
+         Learning networks 2    

Learning networks 2

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Preliminary steps

Let's start as with the previous tutorial:

using MLJ, DataFrames, Random
 @load RidgeRegressor pkg=MultivariateStats
 
 Random.seed!(5) # for reproducibility
diff --git a/__site/getting-started/learning-networks/index.html b/__site/getting-started/learning-networks/index.html
index 18fd2ec4..08ef71e5 100644
--- a/__site/getting-started/learning-networks/index.html
+++ b/__site/getting-started/learning-networks/index.html
@@ -1,4 +1,4 @@
-         Learning networks    

Learning networks

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Preliminary steps

Let's generate a DataFrame with some dummy regression data, let's also load the good old ridge regressor.

using MLJ, DataFrames, Random
+         Learning networks    

Learning networks

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Preliminary steps

Let's generate a DataFrame with some dummy regression data, let's also load the good old ridge regressor.

using MLJ, DataFrames, Random
 @load RidgeRegressor pkg=MultivariateStats
 
 Random.seed!(5) # for reproducibility
diff --git a/__site/getting-started/model-tuning/index.html b/__site/getting-started/model-tuning/index.html
index cbf4d24e..d2e34e13 100644
--- a/__site/getting-started/model-tuning/index.html
+++ b/__site/getting-started/model-tuning/index.html
@@ -1,4 +1,4 @@
-         Tuning a model    

Tuning a model

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Tuning a single hyperparameter

In MLJ, tuning is implemented as a model wrapper. After wrapping a model in a tuning strategy (e.g. cross-validation) and binding the wrapped model to data in a machine, fitting the machine initiates a search for optimal model hyperparameters.

Let's use a decision tree classifier and tune the maximum depth of the tree. As usual, start by loading data and the model

using MLJ, PrettyPrinting
+         Tuning a model    

Tuning a model

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

Tuning a single hyperparameter

In MLJ, tuning is implemented as a model wrapper. After wrapping a model in a tuning strategy (e.g. cross-validation) and binding the wrapped model to data in a machine, fitting the machine initiates a search for optimal model hyperparameters.

Let's use a decision tree classifier and tune the maximum depth of the tree. As usual, start by loading data and the model

using MLJ, PrettyPrinting
 X, y = @load_iris
 @load DecisionTreeClassifier
DecisionTreeClassifier(
     max_depth = -1,
diff --git a/__site/getting-started/stacking/index.html b/__site/getting-started/stacking/index.html
new file mode 100644
index 00000000..0d47429c
--- /dev/null
+++ b/__site/getting-started/stacking/index.html
@@ -0,0 +1,290 @@
+         Stacking    

Stacking

Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save). In stacking one blends the predictions of different regressors or classifiers to gain, in some cases, better performance than naive averaging or majority vote.

Here we illustrate how to build a two-model stack as an MLJ learning network, which we export as a new stand-alone composite model type MyTwoStack. This will make the stack that we build completely re-usable (new data, new models) and means we can apply meta-algorithms, such as performance evaluation and tuning, to the stack, exaclty as we would for any other model.

Our main purpose here is to demonstrate the flexibility of MLJ's composite model interface. Eventually, MLJ will provide built-in composite types or macros to achieve the same results in a few lines, which will suffice for routine stacking tasks.

After defining the MyTwoStack model type, we instantiate it for an application to the Ames House Price data set.

Basic stacking using out-of-sample base learner predictions

A rather general stacking protocol was first described in a 1992 paper by David Wolpert. For a generic introduction to the basic two-layer stack described here, see this blog post of Burak Himmetoglu.

A basic stack consists of a number of base learners (two, in this illustration) and a single adjudicating model.

When a stacked model is called to make a prediction, the individual predictions of the base learners are made the columns of an input table for the adjudicating model, which then outputs the final prediction. However, it is crucial to understand that the flow of data during training is not the same.

The base model predictions used to train the adjudicating model are not the predictions of the base learners fitted to all the training data. Rather, to prevent the adjudicator giving too much weight to the base learners with low training error, the input data is first split into a number of folds (as in cross-validation), a base learner is trained on each fold complement individually, and corresponding predictions on the folds are spliced together to form a full-length prediction called the out-of-sample.prediction.

For illustrative purposes we use just three folds. Each base learner will get three separate machines, for training on each fold complement, and a fourth machine, trained on all the supplied data, for use in the prediction flow.

We build the learning network with dummy data at the source nodes, so the reader inspect the workings of the network as it is built (by calling fit! on nodes, and by calling the nodes themselves). As usual, this data is not seen by the exported composite model type, and the component models we choose are just default values for the hyperparameters of the composite model.

using MLJ, PyPlot
+import Random.seed!
+seed!(1234)
MersenneTwister(UInt32[0x000004d2]) @ 1002
+

Some models we will use:

+
linear = @load LinearRegressor pkg=MLJLinearModels
+ridge = @load RidgeRegressor pkg=MultivariateStats; ridge.lambda = 0.01
+knn = @load KNNRegressor; knn.K = 4
+tree = @load DecisionTreeRegressor; min_samples_leaf=1
+forest = @load RandomForestRegressor pkg=DecisionTree; forest.n_trees=500
+svm = @load SVMRegressor;
+

Warm-up exercise: Define a model type to average predictions

+

Let's define a composite model type MyAverageTwo that averages the predictions of two deterministic regressors. Here's the learning network:

+
X = source()
+y = source(kind=:target)
+
+model1 = linear
+model2 = knn
+
+m1 = machine(model1, X, y)
+y1 = predict(m1, X)
+
+m2 = machine(model2, X, y)
+y2 = predict(m2, X)
+
+yhat = 0.5*y1 + 0.5*y2
Node @ 7…82 = +(#80(predict(1…58, 2…95)), #80(predict(5…88, 2…95)))
+

And the macro call to define MyAverageTwo and an instance average_two:

+
avg = @from_network MyAverageTwo(regressor1=model1,
+                                 regressor2=model2) <= yhat
MyAverageTwo(
+    regressor1 = LinearRegressor(
+            fit_intercept = true,
+            solver = nothing),
+    regressor2 = KNNRegressor(
+            K = 4,
+            algorithm = :kdtree,
+            metric = Distances.Euclidean(0.0),
+            leafsize = 10,
+            reorder = true,
+            weights = :uniform)) @ 1…06
+

Evaluating this average model on the Boston data set, and comparing with the base model predictions:

+
function print_performance(model, data...)
+    e = evaluate(model, data...;
+                 resampling=CV(rng=1234, nfolds=8),
+                 measure=rms,
+                 verbosity=0)
+    μ = round(e.measurement[1], sigdigits=5)
+    ste = round(std(e.per_fold[1])/sqrt(8), digits=5)
+    println("\n $model =  ± $(2*ste)")
+end;
+
+X, y = @load_boston
+
+print_performance(linear, X, y)
+print_performance(knn, X, y)
+print_performance(avg, X, y)

+ LinearRegressor @ 5…31 = 4.9779 ± 0.90056
+
+ KNNRegressor @ 1…34 = 6.3794 ± 0.89744
+
+ MyAverageTwo @ 1…06 = 4.9802 ± 0.94746
+
+

Stacking proper

Helper functions:

+

To generate folds for generating out-of-sample predictions, we define

+
folds(data, nfolds) =
+    partition(1:nrows(data), (1/nfolds for i in 1:(nfolds-1))...);
+

For example, we have:

+
f = folds(1:10, 3)
([1, 2, 3], [4, 5, 6], [7, 8, 9, 10])
+

In our learning network, the folds will depend on the input data, which will be wrapped as a source node. We therefore need to overload the folds function for nodes:

+
folds(X::AbstractNode, nfolds) = node(XX -> folds(XX, nfolds), X);
+

It will also be convenient to use the MLJ method restrict(X, f, i) that restricts data X to the ith element (fold) of f, and corestrict(X, f, i) that restricts to the corresponding fold complement (the concatenation of all but the ith fold).

+

For example, we have:

+
corestrict(string.(1:10), f, 2)
7-element Array{String,1}:
+ "1"
+ "2"
+ "3"
+ "7"
+ "8"
+ "9"
+ "10"
+

Overloading these functions for nodes:

+
MLJ.restrict(X::AbstractNode, f::AbstractNode, i) =
+    node((XX, ff) -> restrict(XX, ff, i), X, f);
+MLJ.corestrict(X::AbstractNode, f::AbstractNode, i) =
+    node((XX, ff) -> corestrict(XX, ff, i), X, f);
+

All the other data manipulations we will need (vcat, hcat, MLJ.table) are already overloaded to work with nodes.

+

Choose some test data (optional) and some component models (defaults for the composite model):

+
figure(figsize=(8,6))
+steps(x) = x < -3/2 ? -1 : (x < 3/2 ? 0 : 1)
+x = Float64[-4, -1, 2, -3, 0, 3, -2, 1, 4]
+Xraw = (x = x, )
+yraw = steps.(x);
+idxsort = sortperm(x)
+xsort = x[idxsort]
+ysort = yraw[idxsort]
+step(xsort, ysort, label="truth", where="mid")
+plot(x, yraw, ls="none", marker="o", label="data")
+xlim(-4.5, 4.5)
+legend()
+ +

Some models to stack:

+
model1 = linear
+model2 = knn
KNNRegressor(
+    K = 4,
+    algorithm = :kdtree,
+    metric = Distances.Euclidean(0.0),
+    leafsize = 10,
+    reorder = true,
+    weights = :uniform) @ 1…34
+

The adjudicating model:

+
judge = linear
LinearRegressor(
+    fit_intercept = true,
+    solver = nothing) @ 5…31
+

Define the training nodes

+

Let's instantiate some input and target source nodes for the learning network, wrapping the play data defined above:

+

Wrapped as source node:

+
X = source(Xraw)
+y = source(yraw; kind=:target)
Source{:target} @ 1…80
+
+

Our first internal node represents the three folds (vectors of row indices) for creating the out-of-sample predictions:

+
f = folds(X, 3)
+f()
([1, 2, 3], [4, 5, 6], [7, 8, 9])
+

Constructing machines for training model1 on each fold-complement:

+
m11 = machine(model1, corestrict(X, f, 1), corestrict(y, f, 1))
+m12 = machine(model1, corestrict(X, f, 2), corestrict(y, f, 2))
+m13 = machine(model1, corestrict(X, f, 3), corestrict(y, f, 3))
NodalMachine @ 2…93 = machine(LinearRegressor @ 5…31, 8…47, 6…53)
+

Define each out-of-sample prediction of model1:

+
y11 = predict(m11, restrict(X, f, 1));
+y12 = predict(m12, restrict(X, f, 2));
+y13 = predict(m13, restrict(X, f, 3));
+

Splice together the out-of-sample predictions for model1:

+
y1_oos = vcat(y11, y12, y13);
+

Optionally, to check our network so far, we can fit and plot y1_oos:

+
fit!(y1_oos, verbosity=0)
+
+figure(figsize=(8,6))
+step(xsort, ysort, label="truth", where="mid")
+plot(x, y1_oos(), ls="none", marker="o", label="linear oos")
+ +

We now repeat the procedure for the other model:

+
m21 = machine(model2, corestrict(X, f, 1), corestrict(y, f, 1))
+m22 = machine(model2, corestrict(X, f, 2), corestrict(y, f, 2))
+m23 = machine(model2, corestrict(X, f, 3), corestrict(y, f, 3))
+y21 = predict(m21, restrict(X, f, 1));
+y22 = predict(m22, restrict(X, f, 2));
+y23 = predict(m23, restrict(X, f, 3));
+

And testing the knn out-of-sample prediction:

+
y2_oos = vcat(y21, y22, y23);
+fit!(y2_oos, verbosity=0)
+
+figure(figsize=(8,6))
+step(xsort, ysort, label="truth", where="mid")
+plot(x, y2_oos(), ls="none", marker="o", label="knn oos")
+ +

Now that we have the out-of-sample base learner predictions, we are ready to merge them into the adjudicator's input table and construct the machine for training the adjudicator:

+
X_oos = MLJ.table(hcat(y1_oos, y2_oos))
+m_judge = machine(judge, X_oos, y)
NodalMachine @ 1…19 = machine(LinearRegressor @ 5…31, 1…60, 1…80)
+

Are we done with constructing machines? Well, not quite. Recall that when use the stack to make predictions on new data, we will be feeding the adjudicator ordinary predictions on the base learners. But so far, we have only defined machines to train the base learners on fold complements, not on the full data, which we do now:

+
m1 = machine(model1, X, y)
+m2 = machine(model2, X, y)
NodalMachine @ 8…74 = machine(KNNRegressor @ 1…34, 6…44, 1…80)
+

Define nodes still needed for prediction

+

To obtain the final prediction, yhat, we get the base learner predictions, based on training with all data, and feed them to the adjudicator:

+
y1 = predict(m1, X);
+y2 = predict(m2, X);
+X_judge = MLJ.table(hcat(y1, y2))
+yhat = predict(m_judge, X_judge)
Node @ 4…11 = predict(1…19, table(hcat(predict(1…75, 6…44), predict(8…74, 6…44))))
+

Let's check the final prediction node can be fit and called:

+
fit!(yhat, verbosity=0)
+
+figure(figsize=(8,6))
+step(xsort, ysort, label="truth", where="mid")
+plot(x, yhat(), ls="none", marker="o", label="yhat")
+ +

Although of little statistical significance here, we note that stacking gives a lower training error than naive averaging:

+
e1 = rms(y1(), y())
+e2 = rms(y2(), y())
+emean = rms(0.5*y1() + 0.5*y2(), y())
+estack = rms(yhat(), y())
+@show e1 e2 emean estack;
e1 = 0.2581988897471611
+e2 = 0.25
+emean = 0.22126530078919587
+estack = 0.19577994695380313
+
+

Export the learning network as a new model type

+

The learning network (less the data wrapped in the source nodes) amounts to a specification of a new composite model type for two-model stacks, trained with three-fold resampling of base model predictions. Let's create the new type MyTwoModelStack:

+
@from_network MyTwoModelStack(regressor1=model1,
+                              regressor2=model2,
+                              judge=judge) <= yhat
MyTwoModelStack(
+    regressor1 = LinearRegressor(
+            fit_intercept = true,
+            solver = nothing),
+    regressor2 = KNNRegressor(
+            K = 4,
+            algorithm = :kdtree,
+            metric = Distances.Euclidean(0.0),
+            leafsize = 10,
+            reorder = true,
+            weights = :uniform),
+    judge = LinearRegressor(
+            fit_intercept = true,
+            solver = nothing)) @ 1…65
+

And this completes the definition of our re-usable stacking model type.

+

Applying MyTwoModelStack to Ames House Price data

+

Without undertaking any hyperparameter optimization, we evaluate the performance of a random forest and ridge regressor on the well-known Ames House Prices data, and compare the performance with a stack (and simple averaging) using the random forest and ridge regressors as base learners. We then indicate some options for tuning the stack.

+

Data pre-processing

+

Here we use a 12-feature reduced subset of the Ames House Price data set:

+
X0, y0 = @load_reduced_ames;
+

Inspect scitypes:

+
s = schema(X0)
+(names=collect(s.names), scitypes=collect(s.scitypes)) |> pretty
┌──────────────┬───────────────────┐
+│ names        │ scitypes          │
+│ Symbol       │ DataType          │
+│ Unknown      │ Unknown           │
+├──────────────┼───────────────────┤
+│ OverallQual  │ OrderedFactor{10} │
+│ GrLivArea    │ Continuous        │
+│ Neighborhood │ Multiclass{25}    │
+│ x1stFlrSF    │ Continuous        │
+│ TotalBsmtSF  │ Continuous        │
+│ BsmtFinSF1   │ Continuous        │
+│ LotArea      │ Continuous        │
+│ GarageCars   │ Count             │
+│ MSSubClass   │ Multiclass{15}    │
+│ GarageArea   │ Continuous        │
+│ YearRemodAdd │ Count             │
+│ YearBuilt    │ Count             │
+└──────────────┴───────────────────┘
+
+

Coerce counts and ordered factors to continuous:

+
X1 = coerce(X0, :OverallQual => Continuous,
+            :GarageCars => Continuous,
+            :YearRemodAdd => Continuous,
+            :YearBuilt => Continuous);
+

One-hot encode the multiclass:

+
hot_mach = fit!(machine(OneHotEncoder(), X1), verbosity=0)
+X = transform(hot_mach, X1);
+

Check the final scitype:

+
scitype(X)
Table{AbstractArray{Continuous,1}}
+

transform the target:

+
y1 = log.(y0)
+y = transform(fit!(machine(UnivariateStandardizer(), y1),
+                   verbosity=0), y1);
+

Define the stack and compare performance:

+
avg = MyAverageTwo(regressor1=forest,
+                   regressor2=ridge)
+
+
+stack = MyTwoModelStack(regressor1=forest,
+                        regressor2=ridge,
+                        judge=linear)
+
+all_models = [forest, ridge, avg, stack];
+
+for model in all_models
+    print_performance(model, X, y)
+end;

+ RandomForestRegressor @ 1…05 = 0.3625 ± 0.02022
+
+ RidgeRegressor @ 1…79 = 0.33029 ± 0.01908
+
+ MyAverageTwo @ 2…57 = 0.34601 ± 0.01464
+
+ MyTwoModelStack @ 6…91 = 0.33028 ± 0.01938
+
+

Tuning a stack

+

A standard abuse of good data hygiene practice is to optimize stack component models separately and then tune the adjudicating model hyperparameters (using the same resampling of the data) with the base learners fixed. Although more computationally expensive, better generalization might be expected by applying tuning to the stack as a whole, either simultaneously, or in in cheaper sequential steps. Since our stack is a stand-alone model, this is readily implemented.

+

As a proof of concept, let's see how to tune one of the base model hyperparameters, based on performance of the stack as a whole:

+
r = range(stack, :(regressor2.lambda), lower = 1, upper = 20, scale=:log)
+tuned_stack = TunedModel(model=stack,
+                         ranges=r,
+                         tuning=Grid(),
+                         measure=rms,
+                         resampling=Holdout())
+
+mach = fit!(machine(tuned_stack,  X, y), verbosity=0)
+best_stack = fitted_params(mach).best_model
+best_stack.regressor2.lambda
10.27808532802195
+

Let's evaluate the best stack using the same data resampling used to the evaluate the assorted untuned models earlier (now we are neglecting data hygeine!):

+
print_performance(best_stack, X, y)

+ MyTwoModelStack @ 1…18 = 0.32861 ± 0.01914
+
+
+ +
+ +
+ +
+
+ \ No newline at end of file diff --git a/__site/index.html b/__site/index.html index 1878a68b..e83398ec 100644 --- a/__site/index.html +++ b/__site/index.html @@ -1,4 +1,4 @@ - MLJ Tutorials

MLJ Tutorials

Learning by doing

This website offers tutorials for MLJ.jl and related packages. On each tutorial page, you will find a link to download the raw script and the notebook corresponding to the page.

Feedback and PRs are always welcome to help make these tutorials better, from the presentation to the content.

In order to reproduce the environment that was used to generate these tutorials, please download this Project.toml and this Manifest.toml in a folder and, in that folder, do

julia> using Pkg; Pkg.activate("."); Pkg.instantiate();
+ MLJ Tutorials

MLJ Tutorials

Learning by doing

This website offers tutorials for MLJ.jl and related packages. On each tutorial page, you will find a link to download the raw script and the notebook corresponding to the page.

Feedback and PRs are always welcome to help make these tutorials better, from the presentation to the content.

In order to reproduce the environment that was used to generate these tutorials, please download this Project.toml and this Manifest.toml in a folder and, in that folder, do

julia> using Pkg; Pkg.activate("."); Pkg.instantiate();

Elementary data manipulations

If you have some programming experience but are otherwise fairly new to data processing in Julia, you may appreciate the following few tutorials before moving on. In these we provide an introduction to some of the fundamental packages in the Julia data processing universe such as DataFrames, CSV and CategoricalArrays.

@@ -25,12 +25,16 @@

ensemble models (2)

+
  • More on ensembles

    +
  • How to compose models

  • How to build a learning network

  • How to create models from learning networks

    +
  • An extended tutorial on stacking

    +

    Additionally, you can refer to the documentation for more detailed information.

    Introduction to Statistical Learning with MLJ

    @@ -71,7 +75,7 @@

    Franklin.jl. + © Anthony Blaom, Thibaut Lienart and collaborators. Last modified: February 20, 2020. Website built with Franklin.jl.

  • diff --git a/__site/isl/lab-10/index.html b/__site/isl/lab-10/index.html index ea532cb0..83888552 100644 --- a/__site/isl/lab-10/index.html +++ b/__site/isl/lab-10/index.html @@ -1,4 +1,4 @@ - Lab 10 - PCA and Clustering

    Lab 10 - PCA and Clustering

    Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

    Getting started

    using MLJ, RDatasets, Random
    +         Lab 10 - PCA and Clustering    

    Lab 10 - PCA and Clustering

    Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

    Getting started

    using MLJ, RDatasets, Random
     
     data = dataset("datasets", "USArrests")
     names(data)
    5-element Array{Symbol,1}:
    diff --git a/__site/isl/lab-2/index.html b/__site/isl/lab-2/index.html
    index 86647518..6354acff 100644
    --- a/__site/isl/lab-2/index.html
    +++ b/__site/isl/lab-2/index.html
    @@ -1,4 +1,4 @@
    -         Lab 2    

    Lab 2

    Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

    Basic commands

    This is a very brief and rough primer if you're new to Julia and wondering how to do simple things that are relevant for data analysis.

    Defining a vector

    x = [1, 3, 2, 5]
    +         Lab 2    

    Lab 2

    Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

    Basic commands

    This is a very brief and rough primer if you're new to Julia and wondering how to do simple things that are relevant for data analysis.

    Defining a vector

    x = [1, 3, 2, 5]
     @show x
     @show length(x)
    x = [1, 3, 2, 5]
     length(x) = 4
    diff --git a/__site/isl/lab-3/index.html b/__site/isl/lab-3/index.html
    index 6f07dd51..889f29dc 100644
    --- a/__site/isl/lab-3/index.html
    +++ b/__site/isl/lab-3/index.html
    @@ -1,4 +1,4 @@
    -         Lab 3 - Linear Regression    

    Lab 3 - Linear Regression

    Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

    Simple linear regression

    MLJ essentially serves as a unified path to many existing Julia packages each of which provides their own functionalities and models, with their own conventions.

    The simple linear regression demonstrates this. Several packages offer it (beyond just using the backslash operator): here we will use MLJLinearModels but we could also have used GLM, ScikitLearn etc.

    To load the model from a given package use @load ModelName pkg=PackageName

    using MLJ
    +         Lab 3 - Linear Regression    

    Lab 3 - Linear Regression

    Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

    Simple linear regression

    MLJ essentially serves as a unified path to many existing Julia packages each of which provides their own functionalities and models, with their own conventions.

    The simple linear regression demonstrates this. Several packages offer it (beyond just using the backslash operator): here we will use MLJLinearModels but we could also have used GLM, ScikitLearn etc.

    To load the model from a given package use @load ModelName pkg=PackageName

    using MLJ
     
     @load LinearRegressor pkg=MLJLinearModels
    LinearRegressor(
         fit_intercept = true,
    diff --git a/__site/isl/lab-4/index.html b/__site/isl/lab-4/index.html
    index da8d55a9..71761172 100644
    --- a/__site/isl/lab-4/index.html
    +++ b/__site/isl/lab-4/index.html
    @@ -1,4 +1,4 @@
    -         Lab 4 - Logistic Regression, LDA, QDA, KNN    

    Lab 4 - Logistic Regression, LDA, QDA, KNN

    Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

    Stock market data

    Let's load the usual packages and the data

    using MLJ, RDatasets, DataFrames, Statistics
    +         Lab 4 - Logistic Regression, LDA, QDA, KNN    

    Lab 4 - Logistic Regression, LDA, QDA, KNN

    Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

    Stock market data

    Let's load the usual packages and the data

    using MLJ, RDatasets, DataFrames, Statistics
     import StatsBase: countmap
     using PrettyPrinting
     
    diff --git a/__site/isl/lab-5/index.html b/__site/isl/lab-5/index.html
    index 9de8cba0..3dc8707c 100644
    --- a/__site/isl/lab-5/index.html
    +++ b/__site/isl/lab-5/index.html
    @@ -1,4 +1,4 @@
    -         Lab 5 - Cross validation and the bootstrap    

    Lab 5 - Cross validation and the bootstrap

    Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

    Getting started

    using MLJ, RDatasets
    +         Lab 5 - Cross validation and the bootstrap    

    Lab 5 - Cross validation and the bootstrap

    Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

    Getting started

    using MLJ, RDatasets
     auto = dataset("ISLR", "Auto")
     y, X = unpack(auto, ==(:MPG), col->true)
     train, test = partition(eachindex(y), 0.5, shuffle=true, rng=444);

    Note the use of rng= to seed the shuffling of indices so that the results are reproducible.

    Polynomial regression

    @load LinearRegressor pkg=MLJLinearModels
    LinearRegressor(
    diff --git a/__site/isl/lab-6b/index.html b/__site/isl/lab-6b/index.html
    index e208463d..191119ca 100644
    --- a/__site/isl/lab-6b/index.html
    +++ b/__site/isl/lab-6b/index.html
    @@ -1,4 +1,4 @@
    -          Lab 6b - Ridge and Lasso regression    

    Lab 6b - Ridge and Lasso regression

    Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

    Getting started

    using MLJ, RDatasets, PrettyPrinting
    +          Lab 6b - Ridge and Lasso regression    

    Lab 6b - Ridge and Lasso regression

    Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

    Getting started

    using MLJ, RDatasets, PrettyPrinting
     import Distributions
     const D = Distributions
     
    diff --git a/__site/isl/lab-8/index.html b/__site/isl/lab-8/index.html
    index fba477bf..a161dc3a 100644
    --- a/__site/isl/lab-8/index.html
    +++ b/__site/isl/lab-8/index.html
    @@ -1,4 +1,4 @@
    -         Lab 8 - Tree-based models    

    Lab 8 - Tree-based models

    Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

    Getting started

    using MLJ, RDatasets, PrettyPrinting
    +         Lab 8 - Tree-based models    

    Lab 8 - Tree-based models

    Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

    Getting started

    using MLJ, RDatasets, PrettyPrinting
     @load DecisionTreeClassifier pkg=DecisionTree
     
     carseats = dataset("ISLR", "Carseats")
    diff --git a/__site/isl/lab-9/index.html b/__site/isl/lab-9/index.html
    index 56f6f191..c282b6ae 100644
    --- a/__site/isl/lab-9/index.html
    +++ b/__site/isl/lab-9/index.html
    @@ -1,4 +1,4 @@
    -         Lab 9 - Support Vector Machine    

    Lab 9 - Support Vector Machine

    Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

    Getting started

    using MLJ, RDatasets, PrettyPrinting, Random
    false
    + Lab 9 - Support Vector Machine

    Lab 9 - Support Vector Machine

    Download the notebook, the raw script, or the annotated script for this tutorial (right-click on the link and save).

    Getting started

    using MLJ, RDatasets, PrettyPrinting, Random
    false

    We start by generating a 2D cloud of points

    Random.seed!(3203)
     X = randn(20, 2)
    diff --git a/__site/libs/lunr/lunr_index.js b/__site/libs/lunr/lunr_index.js
    index 208acd80..6ee72bfd 100644
    --- a/__site/libs/lunr/lunr_index.js
    +++ b/__site/libs/lunr/lunr_index.js
    @@ -1,2 +1,2 @@
    -const LUNR_DATA = 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  • Intro to Stats Learning
  • diff --git a/_libs/lunr/lunr_index.js b/_libs/lunr/lunr_index.js index 6ee72bfd..306950f8 100644 --- a/_libs/lunr/lunr_index.js +++ b/_libs/lunr/lunr_index.js @@ -1,2 +1,2 @@ -const LUNR_DATA = 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that MLJ has a built in model wrapper called `EnsembleModel` +# for creating bagged ensembles with a few lines of code. + +# ## Definition of composite model type + +using MLJ, PyPlot +import Statistics + +# learning network (composite model spec): + +Xs = source() +ys = source(kind=:target) + +atom = @load DecisionTreeRegressor +atom.n_subfeatures = 4 # to ensure diversity among trained atomic models + +machines = (machine(atom, Xs, ys) for i in 1:100) + +# overload `mean` for nodes: +Statistics.mean(v...) = mean(v) +Statistics.mean(v::AbstractVector{<:AbstractNode}) = node(mean, v...) + +yhat = mean([predict(m, Xs) for m in machines]); + + +# new composite model type and instance: + +one_hundred_models = @from_network OneHundredModels(atom=atom) <= yhat + +# ## Application to data + +X, y = @load_boston; + +# tune regularization parameter for a *single* tree: + +r = range(atom, + :min_samples_split, + lower=2, + upper=100, scale=:log) + +mach = machine(atom, X, y) + +curve = learning_curve!(mach, + range=r, + measure=mav, + resampling=CV(nfolds=9), + verbosity=0) + +plot(curve.parameter_values, curve.measurements) +xlabel(curve.parameter_name) + +savefig(joinpath(@OUTPUT, "e1.svg")) # hide + +# \fig{e1.svg} + +# tune regularization parameter for all trees in ensemble simultaneously: + +r = range(one_hundred_models, + :(atom.min_samples_split), + lower=2, + upper=100, scale=:log) + +mach = machine(one_hundred_models, X, y) + +curve = learning_curve!(mach, + range=r, + measure=mav, + resampling=CV(nfolds=9), + verbosity=0) + +plot(curve.parameter_values, curve.measurements) +xlabel(curve.parameter_name) + +savefig(joinpath(@OUTPUT, "e2.svg")) # hide + +# \fig{e2} + +#- + +PyPlot.close_figs() # hide diff --git a/_literate/A-stacking.jl b/_literate/A-stacking.jl new file mode 100644 index 00000000..7cf86f42 --- /dev/null +++ b/_literate/A-stacking.jl @@ -0,0 +1,405 @@ +# In stacking one blends the predictions of different regressors or +# classifiers to gain, in some cases, better performance than naive +# averaging or majority vote. + +# Here we illustrate how to build a two-model stack as an MLJ learning +# network, which we export as a new stand-alone composite model +# type `MyTwoStack`. This will make the stack that we build completely +# re-usable (new data, new models) and means we can apply +# meta-algorithms, such as performance evaluation and tuning, to the +# stack, exaclty as we would for any other model. + +# Our main purpose here is to demonstrate the flexibility of MLJ's +# composite model interface. Eventually, MLJ will provide built-in +# composite types or macros to achieve the same results in a few +# lines, which will suffice for routine stacking tasks. + +# After defining the `MyTwoStack` model type, we instantiate it for an +# application to the Ames House Price data set. + +# ## Basic stacking using out-of-sample base learner predictions + +# A rather general stacking protocol was first described in a [1992 +# paper](https://www.sciencedirect.com/science/article/abs/pii/S0893608005800231) +# by David Wolpert. For a generic introduction to the basic two-layer +# stack described here, see [this blog +# post](https://burakhimmetoglu.com/2016/12/01/stacking-models-for-improved-predictions/) +# of Burak Himmetoglu. + +# A basic stack consists of a number of base learners (two, in this +# illustration) and a single adjudicating model. + +# When a stacked model is called to make a prediction, the individual +# predictions of the base learners are made the columns of an *input* +# table for the adjudicating model, which then outputs the final +# prediction. However, it is crucial to understand that the flow of +# data *during training* is not the same. + +# The base model predictions used to train the adjudicating model are +# *not* the predictions of the base learners fitted to all the +# training data. Rather, to prevent the adjudicator giving too much +# weight to the base learners with low *training* error, the input +# data is first split into a number of folds (as in cross-validation), +# a base learner is trained on each fold complement individually, and +# corresponding predictions on the folds are spliced together to form +# a full-length prediction called the *out-of-sample.prediction*. + +# For illustrative purposes we use just three folds. Each base learner +# will get three separate machines, for training on each fold +# complement, and a fourth machine, trained on all the supplied data, +# for use in the prediction flow. + +# We build the learning network with dummy data at the source nodes, +# so the reader inspect the workings of the network as it is built (by +# calling `fit!` on nodes, and by calling the nodes themselves). As +# usual, this data is not seen by the exported composite model type, +# and the component models we choose are just default values for the +# hyperparameters of the composite model. + +using MLJ, PyPlot +MLJ.color_off() # hide +import Random.seed! +seed!(1234) + +# Some models we will use: + +linear = @load LinearRegressor pkg=MLJLinearModels +ridge = @load RidgeRegressor pkg=MultivariateStats; ridge.lambda = 0.01 +knn = @load KNNRegressor; knn.K = 4 +tree = @load DecisionTreeRegressor; min_samples_leaf=1 +forest = @load RandomForestRegressor pkg=DecisionTree; forest.n_trees=500 +svm = @load SVMRegressor; + +# ### Warm-up exercise: Define a model type to average predictions + +# Let's define a composite model type `MyAverageTwo` that +# averages the predictions of two deterministic regressors. Here's the learning network: + +X = source() +y = source(kind=:target) + +model1 = linear +model2 = knn + +m1 = machine(model1, X, y) +y1 = predict(m1, X) + +m2 = machine(model2, X, y) +y2 = predict(m2, X) + +yhat = 0.5*y1 + 0.5*y2 + +# And the macro call to define `MyAverageTwo` and an instance `average_two`: + +avg = @from_network MyAverageTwo(regressor1=model1, + regressor2=model2) <= yhat + +# Evaluating this average model on the Boston data set, and comparing +# with the base model predictions: + +function print_performance(model, data...) + e = evaluate(model, data...; + resampling=CV(rng=1234, nfolds=8), + measure=rms, + verbosity=0) + μ = round(e.measurement[1], sigdigits=5) + ste = round(std(e.per_fold[1])/sqrt(8), digits=5) + println("\n $model = $μ ± $(2*ste)") +end; + +X, y = @load_boston + +print_performance(linear, X, y) +print_performance(knn, X, y) +print_performance(avg, X, y) + +# ## Stacking proper +# ### Helper functions: + +# To generate folds for generating out-of-sample predictions, we define + +folds(data, nfolds) = + partition(1:nrows(data), (1/nfolds for i in 1:(nfolds-1))...); + +# For example, we have: +f = folds(1:10, 3) + +# In our learning network, the folds will depend on the input data, +# which will be wrapped as a source node. We therefore need to +# overload the `folds` function for nodes: + +folds(X::AbstractNode, nfolds) = node(XX -> folds(XX, nfolds), X); + +# It will also be convenient to use the MLJ method `restrict(X, f, i)` +# that restricts data `X` to the `i`th element (fold) of `f`, and +# `corestrict(X, f, i)` that restricts to the corresponding fold +# complement (the concatenation of all but the `i`th +# fold). + +# For example, we have: + +corestrict(string.(1:10), f, 2) + +# Overloading these functions for nodes: + +MLJ.restrict(X::AbstractNode, f::AbstractNode, i) = + node((XX, ff) -> restrict(XX, ff, i), X, f); +MLJ.corestrict(X::AbstractNode, f::AbstractNode, i) = + node((XX, ff) -> corestrict(XX, ff, i), X, f); + +# All the other data manipulations we will need (`vcat`, `hcat`, +# `MLJ.table`) are already overloaded to work with nodes. + + +# ### Choose some test data (optional) and some component models (defaults for the composite model): + +figure(figsize=(8,6)) +steps(x) = x < -3/2 ? -1 : (x < 3/2 ? 0 : 1) +x = Float64[-4, -1, 2, -3, 0, 3, -2, 1, 4] +Xraw = (x = x, ) +yraw = steps.(x); +idxsort = sortperm(x) +xsort = x[idxsort] +ysort = yraw[idxsort] +step(xsort, ysort, label="truth", where="mid") +plot(x, yraw, ls="none", marker="o", label="data") +xlim(-4.5, 4.5) +legend() + +savefig(joinpath(@OUTPUT, "s1.svg")) # hide + +# \fig{s1.svg} + +# Some models to stack: + +model1 = linear +model2 = knn + +# The adjudicating model: + +judge = linear + + +# ### Define the training nodes + +# Let's instantiate some input and target source nodes for the +# learning network, wrapping the play data defined above: + +# Wrapped as source node: + +X = source(Xraw) +y = source(yraw; kind=:target) + +# Our first internal node represents the three folds (vectors of row +# indices) for creating the out-of-sample predictions: + +f = folds(X, 3) +f() + +# Constructing machines for training `model1` on each fold-complement: + +m11 = machine(model1, corestrict(X, f, 1), corestrict(y, f, 1)) +m12 = machine(model1, corestrict(X, f, 2), corestrict(y, f, 2)) +m13 = machine(model1, corestrict(X, f, 3), corestrict(y, f, 3)) + +# Define each out-of-sample prediction of `model1`: + +y11 = predict(m11, restrict(X, f, 1)); +y12 = predict(m12, restrict(X, f, 2)); +y13 = predict(m13, restrict(X, f, 3)); + +# Splice together the out-of-sample predictions for model1: + +y1_oos = vcat(y11, y12, y13); + +# Optionally, to check our network so far, we can fit and plot +# `y1_oos`: + +fit!(y1_oos, verbosity=0) + +figure(figsize=(8,6)) +step(xsort, ysort, label="truth", where="mid") +plot(x, y1_oos(), ls="none", marker="o", label="linear oos") + +savefig(joinpath(@OUTPUT, "s2.svg")) # hide + +# \fig{s2.svg} + +# We now repeat the procedure for the other model: + +m21 = machine(model2, corestrict(X, f, 1), corestrict(y, f, 1)) +m22 = machine(model2, corestrict(X, f, 2), corestrict(y, f, 2)) +m23 = machine(model2, corestrict(X, f, 3), corestrict(y, f, 3)) +y21 = predict(m21, restrict(X, f, 1)); +y22 = predict(m22, restrict(X, f, 2)); +y23 = predict(m23, restrict(X, f, 3)); + +# And testing the knn out-of-sample prediction: + +y2_oos = vcat(y21, y22, y23); +fit!(y2_oos, verbosity=0) + +figure(figsize=(8,6)) +step(xsort, ysort, label="truth", where="mid") +plot(x, y2_oos(), ls="none", marker="o", label="knn oos") + +savefig(joinpath(@OUTPUT, "s3.svg")) # hide + +# \fig{s3.svg} + +# Now that we have the out-of-sample base learner predictions, we are +# ready to merge them into the adjudicator's input table and construct +# the machine for training the adjudicator: + +X_oos = MLJ.table(hcat(y1_oos, y2_oos)) +m_judge = machine(judge, X_oos, y) + +# Are we done with constructing machines? Well, not quite. Recall that +# when use the stack to make predictions on new data, we will be +# feeding the adjudicator ordinary predictions on the base +# learners. But so far, we have only defined machines to train the +# base learners on fold complements, not on the full data, which we do +# now: + +m1 = machine(model1, X, y) +m2 = machine(model2, X, y) + + +# ### Define nodes still needed for prediction + +# To obtain the final prediction, `yhat`, we get the base learner +# predictions, based on training with all data, and feed them to the +# adjudicator: +y1 = predict(m1, X); +y2 = predict(m2, X); +X_judge = MLJ.table(hcat(y1, y2)) +yhat = predict(m_judge, X_judge) + +# Let's check the final prediction node can be fit and called: +fit!(yhat, verbosity=0) + +figure(figsize=(8,6)) +step(xsort, ysort, label="truth", where="mid") +plot(x, yhat(), ls="none", marker="o", label="yhat") + +savefig(joinpath(@OUTPUT, "s4.svg")) # hide + +# \fig{s4} + +# Although of little statistical significance here, we note that +# stacking gives a lower *training* error than naive averaging: + +e1 = rms(y1(), y()) +e2 = rms(y2(), y()) +emean = rms(0.5*y1() + 0.5*y2(), y()) +estack = rms(yhat(), y()) +@show e1 e2 emean estack; + + +# ## Export the learning network as a new model type + +# The learning network (less the data wrapped in the source nodes) +# amounts to a specification of a new composite model type for +# two-model stacks, trained with three-fold resampling of base model +# predictions. Let's create the new type `MyTwoModelStack`: + +@from_network MyTwoModelStack(regressor1=model1, + regressor2=model2, + judge=judge) <= yhat + +# And this completes the definition of our re-usable stacking model type. + + +# ## Applying `MyTwoModelStack` to Ames House Price data + +# Without undertaking any hyperparameter optimization, we evaluate the +# performance of a random forest and ridge regressor on the well-known +# Ames House Prices data, and compare the performance with a stack +# (and simple averaging) using the random forest and ridge regressors +# as base learners. We then indicate some options for tuning the +# stack. + +# #### Data pre-processing + +# Here we use a 12-feature reduced subset of the Ames House Price data +# set: + +X0, y0 = @load_reduced_ames; + +# Inspect scitypes: + +s = schema(X0) +(names=collect(s.names), scitypes=collect(s.scitypes)) |> pretty + +# Coerce counts and ordered factors to continuous: + +X1 = coerce(X0, :OverallQual => Continuous, + :GarageCars => Continuous, + :YearRemodAdd => Continuous, + :YearBuilt => Continuous); + +# One-hot encode the multiclass: + +hot_mach = fit!(machine(OneHotEncoder(), X1), verbosity=0) +X = transform(hot_mach, X1); + +# Check the final scitype: + +scitype(X) + +# transform the target: + +y1 = log.(y0) +y = transform(fit!(machine(UnivariateStandardizer(), y1), + verbosity=0), y1); + + +# #### Define the stack and compare performance: + +avg = MyAverageTwo(regressor1=forest, + regressor2=ridge) + + +stack = MyTwoModelStack(regressor1=forest, + regressor2=ridge, + judge=linear) + +all_models = [forest, ridge, avg, stack]; + +for model in all_models + print_performance(model, X, y) +end; + + +# #### Tuning a stack + +# A standard abuse of good data hygiene practice is to optimize stack +# component models *separately* and then tune the adjudicating model +# hyperparameters (using the same resampling of the data) with the +# base learners fixed. Although more computationally expensive, better +# generalization might be expected by applying tuning to the stack as +# a whole, either simultaneously, or in in cheaper sequential +# steps. Since our stack is a stand-alone model, this is readily +# implemented. + +# As a proof of concept, let's see how to tune one of the base model +# hyperparameters, based on performance of the stack as a whole: + +r = range(stack, :(regressor2.lambda), lower = 1, upper = 20, scale=:log) +tuned_stack = TunedModel(model=stack, + ranges=r, + tuning=Grid(), + measure=rms, + resampling=Holdout()) + +mach = fit!(machine(tuned_stack, X, y), verbosity=0) +best_stack = fitted_params(mach).best_model +best_stack.regressor2.lambda + +# Let's evaluate the best stack using the same data resampling used to +# the evaluate the assorted untuned models earlier (now we are neglecting +# data hygeine!): + +print_performance(best_stack, X, y) + +PyPlot.close_figs() # hide diff --git a/getting-started/ensembles-3.md b/getting-started/ensembles-3.md new file mode 100644 index 00000000..1b4e892f --- /dev/null +++ b/getting-started/ensembles-3.md @@ -0,0 +1,6 @@ +@def hascode = true +@def showall = true + +# Ensemble models - extended tutorial + +\tutorial{A-ensembles-3} diff --git a/getting-started/stacking.md b/getting-started/stacking.md new file mode 100644 index 00000000..dada2faa --- /dev/null +++ b/getting-started/stacking.md @@ -0,0 +1,6 @@ +@def hascode = true +@def showall = true + +# Stacking + +\tutorial{A-stacking} diff --git a/index.md b/index.md index 342349da..6afc59ac 100644 --- a/index.md +++ b/index.md @@ -37,9 +37,11 @@ If you are new to MLJ but are familiar with Julia and with Machine Learning, we 1. How to [tune models](/getting-started/model-tuning/) 1. How to [ensemble models](/getting-started/ensembles/) 1. How to [ensemble models (2)](/getting-started/ensembles-2/) +1. More on [ensembles](/getting-started/ensembles-3/) 1. How to [compose models](/getting-started/composing-models/) 1. How to build a [learning network](/getting-started/learning-networks/) 1. How to [create models](/getting-started/learning-networks-2/) from learning networks +1. An extended tutorial on [stacking](/getting-started/stacking/) Additionally, you can refer to the [documentation](https://alan-turing-institute.github.io/MLJ.jl/stable/) for more detailed information.