.. only:: html

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        Click :ref:`here <sphx_glr_download_auto_examples_inspection_plot_permutation_importance_multicollinear.py>`     to download the full example code or to run this example in your browser via Binder
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    .. _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`


.. code-block:: default

    print(__doc__)
    from collections import defaultdict

    import matplotlib.pyplot as plt
    import numpy as np
    from scipy.stats import spearmanr
    from scipy.cluster import hierarchy

    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








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:


.. 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

 Out:

 .. code-block:: none

    Accuracy on test data: 0.97




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.


.. 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_yticklabels(data.feature_names[tree_importance_sorted_idx])
    ax1.set_yticks(tree_indices)
    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:: /auto_examples/inspection/images/sphx_glr_plot_permutation_importance_multicollinear_001.png
    :alt: plot permutation importance multicollinear
    :class: sphx-glr-single-img





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:


.. code-block:: default

    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 8))
    corr = spearmanr(X).correlation
    corr_linkage = hierarchy.ward(corr)
    dendro = hierarchy.dendrogram(
        corr_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:: /auto_examples/inspection/images/sphx_glr_plot_permutation_importance_multicollinear_002.png
    :alt: plot permutation importance multicollinear
    :class: sphx-glr-single-img





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.


.. code-block:: default

    cluster_ids = hierarchy.fcluster(corr_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

 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  3.611 seconds)


.. _sphx_glr_download_auto_examples_inspection_plot_permutation_importance_multicollinear.py:


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