Added per-class probability prediction for random forests

[AlanRace]

Added a function to predict the per-class probability of each class for each observation.

let probabilities = forest.predict_probs(&data).unwrap();

probabilities is a KxC matrix, where K is the number of observations and C is the number of classes. Probabilities are calculated as the fraction of trees in the random forest that predicted the given class.

Answer to #50 for random forests.

[VolodymyrOrlov]

@AlanRace thank you for your contribution to Smartcore! The change looks good, but you might want to look at clippy warnings as well as increase test coverage to get this code through automatic checks

[Mec-iS]

I have added a test here but there is something wrong, please take a look:
AlanRace#1

[AlanRace]

@Mec-iS Thanks for supplying the test - I am guessing there was a problem due to row-major vs column-major storage of DenseMatrix? Swapping the number of rows and columns in your test and then transposing the matrix results in a passing test.

[codecov-commenter]

Codecov Report

Merging #138 (7f7b2ed) into development (b4a807e) will increase coverage by 0.60%.
The diff coverage is 100.00%.

@@               Coverage Diff               @@
##           development     #138      +/-   ##
===============================================
+ Coverage        83.40%   84.01%   +0.60%     
===============================================
  Files               78       81       +3     
  Lines             8377     8751     +374     
===============================================
+ Hits              6987     7352     +365     
- Misses            1390     1399       +9     

Impacted Files	Coverage Δ
src/ensemble/random_forest_classifier.rs	75.58% <100.00%> (+4.54%)	⬆️
src/linalg/evd.rs	86.06% <0.00%> (ø)
src/linear/lasso_optimizer.rs	94.11% <0.00%> (ø)
src/algorithm/neighbour/mod.rs	78.57% <0.00%> (ø)
src/algorithm/neighbour/distances.rs	66.66% <0.00%> (ø)
src/preprocessing/numerical.rs	88.88% <0.00%> (ø)
src/algorithm/neighbour/fastpair.rs	95.67% <0.00%> (ø)
src/linalg/naive/dense_matrix.rs	80.11% <0.00%> (+0.89%)	⬆️
src/optimization/first_order/lbfgs.rs	94.44% <0.00%> (+1.58%)	⬆️
src/linalg/mod.rs	58.57% <0.00%> (+5.49%)	⬆️
... and 1 more

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[Mec-iS]

thanks @AlanRace

it is probably better to adhere to the DenseMatrix format, so it would be nice for the method to return the transposed values or directly a DenseMatrix.

[AlanRace]

Maybe I am misunderstanding, but predict_probs does return a DenseMatrix.

It looks like DenseMatrix::from_vec (which is called from DenseMatrix::from_array as part of your test) assumes that the given vector is in row-major form, but the entered values in the test are in column-major form.

Would you prefer that the matrix returned from predict_probs is num classes x num observations, rather than the current num observations x num classes?

[Mec-iS]

yeah, probably in the shape returned by from_vector and from_array is handier. thanks again

[Mec-iS]

@morenol @VolodymyrOrlov could you please take a look to the WASM test failing? it looks like we have different results for different targets. Looks like rounding works different for WASM, the results look close but not close enough.

[alexis2804]

Hello guys, when does this fucntion will be available ? I totally need it in order to perform model ensembling !

Thanks a lot

[Mec-iS]

@alexis2804 unfortunately we have problems with some tests, you can take a look at them by fetching this branch

[Mec-iS]

moved to #211 to solve conflicts