Missing random feature selection in Random Forest construction. about ml-from-scratch

[leferrad]

I don't agree with the idea of fitting a RandomForest by selecting the best features from a random subset at each node of a given tree, or at least I didn't understand it. I've just reviewed the code and it seems to behave as correct as I know, and actually it doesn't reuse DecisionTrees as you said so I don't get the problem with the behavior:

1. Here the decision trees are initialized separately by getting instances of the class ClassificationTree and storing them into a list (as in any OOP program, objects are not the same than classes). Therefore, the RF doesn't use the same tree for predictions.
2. Here occurs the sample of feature for each tree, by getting indexes of the whole set of features and fitting the given tree with the selection of those features. Therefore, every tree is fitted with a random selection of features in a separate way.

Let me know the algorithm that you wanted to explain (through a link or a paper citation) to compare the implementations, but so far I think this implementation is correct. In addition, I also congrats for the whole repository, it's great to have a prolix set of implementation of the most important algorithms handled in ML.

[cesar0205]

Both implementations are correct. Erik is using the original feature subset selection procedure proposed by Tin Kam Ho whereas I am refering to the one used by Leo Breiman.

In 1995 Tin Kam Ho published his paper "random decision forests" using a randomly selected subset of features for growing each tree. However in 2001, Leo Breiman published his seminal Random Forests paper, wherein the feature subset is randomly selected at each node within each tree, not at each tree. While Breiman cited Ho, he did not specifically explain the move from tree-level to node-level random feature selection.

Almost all implementations I've seen use the Breiman feature selection at node level instead of tree level. I.E. Elements of Statistical Learning Page 588, https://web.stanford.edu/~hastie/Papers/ESLII.pdf and Sklearn's RandomForestClassifier, https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html