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Random Forest in Machine Learning

Random forest is one of the most amazing machine learning (ML) algorithms invented by Leo Breiman and Adele Cutler back in the last century. It has come down to us in its "original form" (no heuristics have been able to improve it significantly) and is one of the few universal algorithms.

The versatility lies, firstly, in the fact that it is used to solve many problems (according to my estimates, it can be used to solve around 70% of those machine learning problems encountered in practice, if we do not take into account problems with images), and secondly, in the fact that there are random forests for solving problems classification, regression, clustering, anomaly search, feature selection, etc.

This post is a short practical guide for beginners; it serves as a guide to the main parameters of the algorithm with pictures. The test here means the result on the sliding control (5 folds were used to plot the charts), although the conclusions for the hold-out control will be the same. The charts are in the variance and (if there is a second corridor) the max-min corridor. All conclusions and recommendations are generalized and cannot be used for any specific task.

Random forest (RF) is a set of decision trees. In the regression problem, their answers are averaged; in the classification problem, a decision is made by voting by majority. All trees are built independently according to the following scheme:

  • A subsample is selected from the training sample with a sample size (possibly with return) and a tree is built from it (each tree has its own subsample),

  • To build each splitting in the tree, we look through the max_features of random features (for each new splitting - its own random features),

  • We select the best feature and splitting according to it (according to a predetermined criterion). As a rule, a tree is built before the selection is exhausted (until only representatives of one class remain in the leaves), but in modern implementations, there are parameters that limit the height of the tree, the number of objects in the leaves, and the number of objects in the subsample at which the splitting is performed.

It is clear that such a construction scheme corresponds to the main principle of an ensemble (building a machine learning algorithm based on several, in this case, decision trees): the basic algorithms must be proper and diverse (therefore, each tree is built on its own training set and there is an element of randomness when choosing splits).

The scikit-learn library has such a random forest (RF) implementation (I cite it only for the classification task):

RF realization
RF realization

The algorithm works according to the standard scheme adopted in scikit-learn:

random forest realization
random forest realization

Let's describe what the main parameters mean:

Number of trees - n_estimators

The more trees the better the quality, but the RF setup and run times also increase proportionally. Please note that often with an increase in n_estimators, the quality on the training sample increases (it can even reach 100%), and the quality on the test reaches the asymptote (you can estimate how many trees you need).

n estimators
n estimators

Number of features for splitting selection - max_features

The graph of quality on the test versus the value of this parameter is unimodal; it strictly increases during training. As max_features increases, the forest building time increases and the trees become “more uniform”. By default, it equals sqrt(n) in classification problems and n/3 in regression problems. This is the most important parameter! You must set it up first (with a sufficient number of trees in the forest).

max features
max features
max features model
max features model

The minimum number of objects at which splitting is performed - min_samples_split

This parameter is usually not very important and you can leave the default value (2). The quality control chart may look like a "comb" (there is no clear optimum). With an increase in the parameter, the quality of training decreases, and the time for building RF reduces.

min samples split
min samples split
min samples split model
min samples split model

Limit on the number of objects in leaves - min_samples_leaf

Everything that was described min_samples_split is also suitable for describing this parameter. You can often leave the default (1). Note that according to the classics, in regression problems it is recommended to use the value 5 (this is implemented that way in the randomForest library for R, in sklearn it is 1).

min samples leaf
min samples leaf
min samples leaf model
min samples leaf model

Maximum tree depth - max_depth

It is clear that the shallower the depth, the faster the RF builds and works. With an increase in depth, the quality in training increases sharply, but in control it, as a rule, increases. It is recommended to use the maximum depth (unless there are too many objects and very deep trees are obtained, the construction of which takes a long time). When using shallow trees, changing the parameters associated with limiting the number of objects in a leaf and for division does not lead to a significant effect (leaves are already "large"). Shallow trees are recommended for use in tasks with a large number of noise objects (outliers).

max depth
max depth
max depth model
max depth model

Criterion

In essence, this is a very important parameter, but in fact there are no options for choosing. The sklearn regression library implements two criteria, “MSE”, which is an abbreviation of Mean Square Error, and “MAE”, Mean Absolute Error, which correspond to the error functions they minimize. Most tasks use MSE. I cannot compare them yet, because mae appeared quite recently - in version 0.18 (and in my opinion, it is implemented with a bug). For classification, the “Gini” and “entropy” criteria have been implemented. A simple search will help you choose what to use in a specific problem (Gini was used in the author's implementation of the algorithm). 

criterion
criterion
criterion model
criterion model

In the sklearn implementation of a random forest, there is no samplesize parameter that regulates how many objects to sub-sample for building each tree. There is such a parameter in the R-implementation, but, in fact, it is often optimal to choose from the entire sample. It is also recommended to choose a subsample with the return: bootstrap = True (this is the bootstrap aggregating).

Last words - a bit of advice

By default, n_jobs = 1 in sklearn methods, i.e. a random forest is built on one processor. If you want to speed up the build significantly, use n_jobs = -1 (build on as many processors as possible). To build reproducible experiments, use the pseudo-random number generator preset: random_state.

P.S. The RF method is also good in that when constructing a forest, in parallel, the so-called oob-estimate of the quality of the algorithm can be calculated (which is very accurate and is obtained not at the expense of the division into training / test), oob-answers algorithms (answers that the algorithm would produce on the training set , if “it didn’t train on it”), the importance of the features is assessed. Finally, do not forget about the full enumeration of parameter values ​​(if there are not that many objects in the task).

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