Feature importances with a forest of trees

This example shows the use of a forest of trees to evaluate the importance of features on an artificial classification task. The blue bars are the feature importances of the forest, along with their inter-trees variability represented by the error bars.

As expected, the plot suggests that 3 features are informative, while the remaining are not.

import matplotlib.pyplot as plt

Data generation and model fitting

We generate a synthetic dataset with only 3 informative features. We will explicitly not shuffle the dataset to ensure that the informative features will correspond to the three first columns of X. In addition, we will split our dataset into training and testing subsets.

from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split

X, y = make_classification(
    n_samples=1000,
    n_features=10,
    n_informative=3,
    n_redundant=0,
    n_repeated=0,
    n_classes=2,
    random_state=0,
    shuffle=False,
)
X_train, X_test, y_train, y_test = train_test_split(X, y, stratify=y, random_state=42)

A random forest classifier will be fitted to compute the feature importances.

from sklearn.ensemble import RandomForestClassifier

feature_names = [f"feature {i}" for i in range(X.shape[1])]
forest = RandomForestClassifier(random_state=0)
forest.fit(X_train, y_train)

RandomForestClassifier(random_state=0)

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Feature importance based on mean decrease in impurity

Feature importances are provided by the fitted attribute feature_importances_ and they are computed as the mean and standard deviation of accumulation of the impurity decrease within each tree.

Warning

Impurity-based feature importances can be misleading for high cardinality features (many unique values). See Permutation feature importance as an alternative below.

import time

import numpy as np

start_time = time.time()
importances = forest.feature_importances_
std = np.std([tree.feature_importances_ for tree in forest.estimators_], axis=0)
elapsed_time = time.time() - start_time

print(f"Elapsed time to compute the importances: {elapsed_time:.3f} seconds")

Elapsed time to compute the importances: 0.005 seconds

Let’s plot the impurity-based importance.

import pandas as pd

forest_importances = pd.Series(importances, index=feature_names)

fig, ax = plt.subplots()
forest_importances.plot.bar(yerr=std, ax=ax)
ax.set_title("Feature importances using MDI")
ax.set_ylabel("Mean decrease in impurity")
fig.tight_layout()

We observe that, as expected, the three first features are found important.

Feature importance based on feature permutation

Permutation feature importance overcomes limitations of the impurity-based feature importance: they do not have a bias toward high-cardinality features and can be computed on a left-out test set.

from sklearn.inspection import permutation_importance

start_time = time.time()
result = permutation_importance(
    forest, X_test, y_test, n_repeats=10, random_state=42, n_jobs=2
)
elapsed_time = time.time() - start_time
print(f"Elapsed time to compute the importances: {elapsed_time:.3f} seconds")

forest_importances = pd.Series(result.importances_mean, index=feature_names)

Elapsed time to compute the importances: 0.521 seconds

The computation for full permutation importance is more costly. Features are shuffled n times and the model refitted to estimate the importance of it. Please see Permutation feature importance for more details. We can now plot the importance ranking.

fig, ax = plt.subplots()
forest_importances.plot.bar(yerr=result.importances_std, ax=ax)
ax.set_title("Feature importances using permutation on full model")
ax.set_ylabel("Mean accuracy decrease")
fig.tight_layout()
plt.show()

The same features are detected as most important using both methods. Although the relative importances vary. As seen on the plots, MDI is less likely than permutation importance to fully omit a feature.