polynomial regressor updated reference page

doc/PolynomialRegressor.rst

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+:digest: Polynomial regression on data sets.
+:species: data
+:sc-categories: Machine Learning
+:sc-related: 
+:see-also: KNNRegressor, DataSet, MLPClassifier
+:description: 
+
+    Perform regression between :fluid-obj:`DataSet`\s using N parallel 1-to-1 polynomial regressors in one object.
+
+:discussion:
+
+    A polynomial regressor is a very simple algorithm that, given a set of input-output pairs - ``x`` to ``y``, for example - will find the line of best fit for that data. Linear regression is a special case when the ``degree`` of the polynomial is ``1``, meaning the line of best fit will be straight.
+
+    Essentially, each element of each input is mapped to the corresponding element of the same output, hence it needing to be an N-to-N corpus, which is one limitation of this algorithm.
+    Tikhonov regularisation is an improvement of this algorithm, which compensates for noisy data and reduces overfitting in certain situations, a good explanation of how this works can be found on wikipedia (https://en.wikipedia.org/wiki/Ridge_regression#Tikhonov_regularization)
+
+:control degree:
+
+    An integer that specifies the degree \(highest power of x\) that the fit polynomial will have; e.g. a degree of 2 means that the polynomial will have a form ``y = \alpha + \beta x + \gamma x^2``. Therefore the higher the degree, the closer the output will get to the original data (until it begins overfitting).
+
+:control tikhonov:
+
+    A floating point value that describes the strength of the Tikhonov filter, namely how much the algorithm is penalised for overfitting to the data
+
+:message fit:
+
+   :arg sourceDataSet: Source data
+
+   :arg targetDataSet: Target data
+
+   Fit the polynomial to map between a source and target :fluid-obj:`DataSet`
+
+:message predict:
+
+   :arg sourceDataSet: Input :fluid-obj:`DataSet`
+
+   :arg targetDataSet: Output :fluid-obj:`DataSet`
+
+   Apply the regressed mapping to a :fluid-obj:`DataSet` and predict the output value for each point
+
+:message predictPoint:
+
+   :arg sourceBuffer: Input point
+
+   :arg targetBuffer: Output point
+
+   Apply the regressed mapping to a single data point in a |buffer|
+
+:message clear:
+
+   This will erase all the learned polynomials.
+
+:message print:
+
+    Print object information to the console.
+
+:message read:
+
+    :arg fileName: file to read from (optional, will prompt if not present)
+
+    load regressed polynomials from a json file on disk
+
+:message write:
+
+    :arg fileName: file to write to (optional, will prompt if not present)
+
+    write current regression to a json file on disk

example-code/sc/PolynomialRegressor.scd

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+code::
+s.boot;
+
+// 10 random points and their square
+~somepoints = 10.collect{var x = 1.0.rand; [x, x**2]}.flop
+
+// load the ins and the outs in 1D datasets
+~in = FluidDataSet(s).load(Dictionary.newFrom(["cols", 1, "data", Dictionary.newFrom(~somepoints[0].collect{|j,i|[i.asSymbol, j]}.flat)]))
+
+~out = FluidDataSet(s).load(Dictionary.newFrom(["cols", 1, "data", Dictionary.newFrom(~somepoints[1].collect{|j,i|[i.asSymbol, j]}.flat)]))
+
+~in.print;~out.print
+
+~polyreg = FluidPolynomialRegressor(s);
+
+~polyreg.fit(~in, ~out, {\done.postln});
+
+// 100 points to draw the function
+
+~question = FluidDataSet(s).load(Dictionary.newFrom(["cols", 1, "data", Dictionary.newFrom(100.collect{|i|[i,i/100]}.flat)]))
+~answer = FluidDataSet(s)
+
+~polyreg.predict(~question, ~answer, {\done.postln});
+
+~arrayedanswer = Array.fill(100,0)
+~answer.dump{|x|x["data"].keysValuesDo{|k,v|~arrayedanswer[k.asInteger]=v}}
+~arrayedanswer.flat.plot
+
+//compare with the real function
+100.collect{|x|(x/100)**2}.plot
+::