Consider the following training/test split of the data. Construct a random forest regressor and identify the optimal subset size \(m\) in the sense of \(R^{2}\) score (see Remark \(8.3)\).

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import numpy as np from sklearn.datasets import make friedmanl from sklearn.tree import DecisionTreeRegressor from sklearn.model_selection import train_test_split from sklearn.metrics import r2_score # create regression problem n_points 1000 points x, y = make_friedmanl (n_samples-n_points, n_features=15, noise 1.0, random_state=100) #split to train/test set. x_train, x_test, y_train, y_test = \ train_test_split(x, y, test_size=0.33, random_state=100)