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.. rst-class:: sphx-glr-example-title
.. _sphx_glr_auto_examples_inspection_plot_permutation_importance_multicollinear.py:
=================================================================
Permutation Importance with Multicollinear or Correlated Features
=================================================================
In this example, we compute the permutation importance on the Wisconsin
breast cancer dataset using :func:`~sklearn.inspection.permutation_importance`.
The :class:`~sklearn.ensemble.RandomForestClassifier` can easily get about 97%
accuracy on a test dataset. Because this dataset contains multicollinear
features, the permutation importance will show that none of the features are
important. One approach to handling multicollinearity is by performing
hierarchical clustering on the features' Spearman rank-order correlations,
picking a threshold, and keeping a single feature from each cluster.
.. note::
See also
:ref:`sphx_glr_auto_examples_inspection_plot_permutation_importance.py`
.. GENERATED FROM PYTHON SOURCE LINES 20-34
.. code-block:: default
from collections import defaultdict
import matplotlib.pyplot as plt
import numpy as np
from scipy.stats import spearmanr
from scipy.cluster import hierarchy
from scipy.spatial.distance import squareform
from sklearn.datasets import load_breast_cancer
from sklearn.ensemble import RandomForestClassifier
from sklearn.inspection import permutation_importance
from sklearn.model_selection import train_test_split
.. GENERATED FROM PYTHON SOURCE LINES 35-39
Random Forest Feature Importance on Breast Cancer Data
------------------------------------------------------
First, we train a random forest on the breast cancer dataset and evaluate
its accuracy on a test set:
.. GENERATED FROM PYTHON SOURCE LINES 39-47
.. code-block:: default
data = load_breast_cancer()
X, y = data.data, data.target
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)
clf = RandomForestClassifier(n_estimators=100, random_state=42)
clf.fit(X_train, y_train)
print("Accuracy on test data: {:.2f}".format(clf.score(X_test, y_test)))
.. rst-class:: sphx-glr-script-out
.. code-block:: none
Accuracy on test data: 0.97
.. GENERATED FROM PYTHON SOURCE LINES 48-55
Next, we plot the tree based feature importance and the permutation
importance. The permutation importance plot shows that permuting a feature
drops the accuracy by at most `0.012`, which would suggest that none of the
features are important. This is in contradiction with the high test accuracy
computed above: some feature must be important. The permutation importance
is calculated on the training set to show how much the model relies on each
feature during training.
.. GENERATED FROM PYTHON SOURCE LINES 55-74
.. code-block:: default
result = permutation_importance(clf, X_train, y_train, n_repeats=10, random_state=42)
perm_sorted_idx = result.importances_mean.argsort()
tree_importance_sorted_idx = np.argsort(clf.feature_importances_)
tree_indices = np.arange(0, len(clf.feature_importances_)) + 0.5
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 8))
ax1.barh(tree_indices, clf.feature_importances_[tree_importance_sorted_idx], height=0.7)
ax1.set_yticks(tree_indices)
ax1.set_yticklabels(data.feature_names[tree_importance_sorted_idx])
ax1.set_ylim((0, len(clf.feature_importances_)))
ax2.boxplot(
result.importances[perm_sorted_idx].T,
vert=False,
labels=data.feature_names[perm_sorted_idx],
)
fig.tight_layout()
plt.show()
.. image-sg:: /auto_examples/inspection/images/sphx_glr_plot_permutation_importance_multicollinear_001.png
:alt: plot permutation importance multicollinear
:srcset: /auto_examples/inspection/images/sphx_glr_plot_permutation_importance_multicollinear_001.png
:class: sphx-glr-single-img
.. GENERATED FROM PYTHON SOURCE LINES 75-83
Handling Multicollinear Features
--------------------------------
When features are collinear, permutating one feature will have little
effect on the models performance because it can get the same information
from a correlated feature. One way to handle multicollinear features is by
performing hierarchical clustering on the Spearman rank-order correlations,
picking a threshold, and keeping a single feature from each cluster. First,
we plot a heatmap of the correlated features:
.. GENERATED FROM PYTHON SOURCE LINES 83-107
.. code-block:: default
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 8))
corr = spearmanr(X).correlation
# Ensure the correlation matrix is symmetric
corr = (corr + corr.T) / 2
np.fill_diagonal(corr, 1)
# We convert the correlation matrix to a distance matrix before performing
# hierarchical clustering using Ward's linkage.
distance_matrix = 1 - np.abs(corr)
dist_linkage = hierarchy.ward(squareform(distance_matrix))
dendro = hierarchy.dendrogram(
dist_linkage, labels=data.feature_names.tolist(), ax=ax1, leaf_rotation=90
)
dendro_idx = np.arange(0, len(dendro["ivl"]))
ax2.imshow(corr[dendro["leaves"], :][:, dendro["leaves"]])
ax2.set_xticks(dendro_idx)
ax2.set_yticks(dendro_idx)
ax2.set_xticklabels(dendro["ivl"], rotation="vertical")
ax2.set_yticklabels(dendro["ivl"])
fig.tight_layout()
plt.show()
.. image-sg:: /auto_examples/inspection/images/sphx_glr_plot_permutation_importance_multicollinear_002.png
:alt: plot permutation importance multicollinear
:srcset: /auto_examples/inspection/images/sphx_glr_plot_permutation_importance_multicollinear_002.png
:class: sphx-glr-single-img
.. GENERATED FROM PYTHON SOURCE LINES 108-113
Next, we manually pick a threshold by visual inspection of the dendrogram
to group our features into clusters and choose a feature from each cluster to
keep, select those features from our dataset, and train a new random forest.
The test accuracy of the new random forest did not change much compared to
the random forest trained on the complete dataset.
.. GENERATED FROM PYTHON SOURCE LINES 113-129
.. code-block:: default
cluster_ids = hierarchy.fcluster(dist_linkage, 1, criterion="distance")
cluster_id_to_feature_ids = defaultdict(list)
for idx, cluster_id in enumerate(cluster_ids):
cluster_id_to_feature_ids[cluster_id].append(idx)
selected_features = [v[0] for v in cluster_id_to_feature_ids.values()]
X_train_sel = X_train[:, selected_features]
X_test_sel = X_test[:, selected_features]
clf_sel = RandomForestClassifier(n_estimators=100, random_state=42)
clf_sel.fit(X_train_sel, y_train)
print(
"Accuracy on test data with features removed: {:.2f}".format(
clf_sel.score(X_test_sel, y_test)
)
)
.. rst-class:: sphx-glr-script-out
.. code-block:: none
Accuracy on test data with features removed: 0.97
.. rst-class:: sphx-glr-timing
**Total running time of the script:** ( 0 minutes 3.908 seconds)
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