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.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/inspection/plot_permutation_importance.py"
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.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_inspection_plot_permutation_importance.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_inspection_plot_permutation_importance.py:


================================================================
Permutation Importance vs Random Forest Feature Importance (MDI)
================================================================

In this example, we will compare the impurity-based feature importance of
:class:`~sklearn.ensemble.RandomForestClassifier` with the
permutation importance on the titanic dataset using
:func:`~sklearn.inspection.permutation_importance`. We will show that the
impurity-based feature importance can inflate the importance of numerical
features.

Furthermore, the impurity-based feature importance of random forests suffers
from being computed on statistics derived from the training dataset: the
importances can be high even for features that are not predictive of the target
variable, as long as the model has the capacity to use them to overfit.

This example shows how to use Permutation Importances as an alternative that
can mitigate those limitations.

.. rubric:: References

* :doi:`L. Breiman, "Random Forests", Machine Learning, 45(1), 5-32,
  2001. <10.1023/A:1010933404324>`

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.. code-block:: Python


    # Authors: The scikit-learn developers
    # SPDX-License-Identifier: BSD-3-Clause








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Data Loading and Feature Engineering
------------------------------------
Let's use pandas to load a copy of the titanic dataset. The following shows
how to apply separate preprocessing on numerical and categorical features.

We further include two random variables that are not correlated in any way
with the target variable (``survived``):

- ``random_num`` is a high cardinality numerical variable (as many unique
  values as records).
- ``random_cat`` is a low cardinality categorical variable (3 possible
  values).

.. GENERATED FROM PYTHON SOURCE LINES 44-60

.. code-block:: Python

    import numpy as np

    from sklearn.datasets import fetch_openml
    from sklearn.model_selection import train_test_split

    X, y = fetch_openml("titanic", version=1, as_frame=True, return_X_y=True)
    rng = np.random.RandomState(seed=42)
    X["random_cat"] = rng.randint(3, size=X.shape[0])
    X["random_num"] = rng.randn(X.shape[0])

    categorical_columns = ["pclass", "sex", "embarked", "random_cat"]
    numerical_columns = ["age", "sibsp", "parch", "fare", "random_num"]

    X = X[categorical_columns + numerical_columns]
    X_train, X_test, y_train, y_test = train_test_split(X, y, stratify=y, random_state=42)



.. rst-class:: sphx-glr-script-out

.. code-block:: pytb

    Traceback (most recent call last):
      File "$BUILD_DIR/examples/inspection/plot_permutation_importance.py", line 49, in <module>
        X, y = fetch_openml("titanic", version=1, as_frame=True, return_X_y=True)
               ~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
      File "$BUILD_DIR/.pybuild/cpython3_3.13/build/sklearn/utils/_param_validation.py", line 218, in wrapper
        return func(*args, **kwargs)
      File "$BUILD_DIR/.pybuild/cpython3_3.13/build/sklearn/datasets/_openml.py", line 998, in fetch_openml
        raise TimeoutError('Debian Policy Section 4.9 prohibits network access during build')
    TimeoutError: Debian Policy Section 4.9 prohibits network access during build




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We define a predictive model based on a random forest. Therefore, we will make
the following preprocessing steps:

- use :class:`~sklearn.preprocessing.OrdinalEncoder` to encode the
  categorical features;
- use :class:`~sklearn.impute.SimpleImputer` to fill missing values for
  numerical features using a mean strategy.

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.. code-block:: Python

    from sklearn.compose import ColumnTransformer
    from sklearn.ensemble import RandomForestClassifier
    from sklearn.impute import SimpleImputer
    from sklearn.pipeline import Pipeline
    from sklearn.preprocessing import OrdinalEncoder

    categorical_encoder = OrdinalEncoder(
        handle_unknown="use_encoded_value", unknown_value=-1, encoded_missing_value=-1
    )
    numerical_pipe = SimpleImputer(strategy="mean")

    preprocessing = ColumnTransformer(
        [
            ("cat", categorical_encoder, categorical_columns),
            ("num", numerical_pipe, numerical_columns),
        ],
        verbose_feature_names_out=False,
    )

    rf = Pipeline(
        [
            ("preprocess", preprocessing),
            ("classifier", RandomForestClassifier(random_state=42)),
        ]
    )
    rf.fit(X_train, y_train)


.. GENERATED FROM PYTHON SOURCE LINES 96-101

Accuracy of the Model
---------------------
Before inspecting the feature importances, it is important to check that
the model predictive performance is high enough. Indeed, there would be little
interest in inspecting the important features of a non-predictive model.

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.. code-block:: Python


    print(f"RF train accuracy: {rf.score(X_train, y_train):.3f}")
    print(f"RF test accuracy: {rf.score(X_test, y_test):.3f}")


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Here, one can observe that the train accuracy is very high (the forest model
has enough capacity to completely memorize the training set) but it can still
generalize well enough to the test set thanks to the built-in bagging of
random forests.

It might be possible to trade some accuracy on the training set for a
slightly better accuracy on the test set by limiting the capacity of the
trees (for instance by setting ``min_samples_leaf=5`` or
``min_samples_leaf=10``) so as to limit overfitting while not introducing too
much underfitting.

However, let us keep our high capacity random forest model for now so that we can
illustrate some pitfalls about feature importance on variables with many
unique values.

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Tree's Feature Importance from Mean Decrease in Impurity (MDI)
--------------------------------------------------------------
The impurity-based feature importance ranks the numerical features to be the
most important features. As a result, the non-predictive ``random_num``
variable is ranked as one of the most important features!

This problem stems from two limitations of impurity-based feature
importances:

- impurity-based importances are biased towards high cardinality features;
- impurity-based importances are computed on training set statistics and
  therefore do not reflect the ability of feature to be useful to make
  predictions that generalize to the test set (when the model has enough
  capacity).

The bias towards high cardinality features explains why the `random_num` has
a really large importance in comparison with `random_cat` while we would
expect that both random features have a null importance.

The fact that we use training set statistics explains why both the
`random_num` and `random_cat` features have a non-null importance.

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.. code-block:: Python

    import pandas as pd

    feature_names = rf[:-1].get_feature_names_out()

    mdi_importances = pd.Series(
        rf[-1].feature_importances_, index=feature_names
    ).sort_values(ascending=True)


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.. code-block:: Python

    ax = mdi_importances.plot.barh()
    ax.set_title("Random Forest Feature Importances (MDI)")
    ax.figure.tight_layout()


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As an alternative, the permutation importances of ``rf`` are computed on a
held out test set. This shows that the low cardinality categorical feature,
`sex` and `pclass` are the most important features. Indeed, permuting the
values of these features will lead to the most decrease in accuracy score of the
model on the test set.

Also, note that both random features have very low importances (close to 0) as
expected.

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.. code-block:: Python

    from sklearn.inspection import permutation_importance

    result = permutation_importance(
        rf, X_test, y_test, n_repeats=10, random_state=42, n_jobs=2
    )

    sorted_importances_idx = result.importances_mean.argsort()
    importances = pd.DataFrame(
        result.importances[sorted_importances_idx].T,
        columns=X.columns[sorted_importances_idx],
    )
    ax = importances.plot.box(vert=False, whis=10)
    ax.set_title("Permutation Importances (test set)")
    ax.axvline(x=0, color="k", linestyle="--")
    ax.set_xlabel("Decrease in accuracy score")
    ax.figure.tight_layout()


.. GENERATED FROM PYTHON SOURCE LINES 183-188

It is also possible to compute the permutation importances on the training
set. This reveals that `random_num` and `random_cat` get a significantly
higher importance ranking than when computed on the test set. The difference
between those two plots is a confirmation that the RF model has enough
capacity to use that random numerical and categorical features to overfit.

.. GENERATED FROM PYTHON SOURCE LINES 188-203

.. code-block:: Python

    result = permutation_importance(
        rf, X_train, y_train, n_repeats=10, random_state=42, n_jobs=2
    )

    sorted_importances_idx = result.importances_mean.argsort()
    importances = pd.DataFrame(
        result.importances[sorted_importances_idx].T,
        columns=X.columns[sorted_importances_idx],
    )
    ax = importances.plot.box(vert=False, whis=10)
    ax.set_title("Permutation Importances (train set)")
    ax.axvline(x=0, color="k", linestyle="--")
    ax.set_xlabel("Decrease in accuracy score")
    ax.figure.tight_layout()


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We can further retry the experiment by limiting the capacity of the trees
to overfit by setting `min_samples_leaf` at 20 data points.

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.. code-block:: Python

    rf.set_params(classifier__min_samples_leaf=20).fit(X_train, y_train)


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Observing the accuracy score on the training and testing set, we observe that
the two metrics are very similar now. Therefore, our model is not overfitting
anymore. We can then check the permutation importances with this new model.

.. GENERATED FROM PYTHON SOURCE LINES 212-215

.. code-block:: Python

    print(f"RF train accuracy: {rf.score(X_train, y_train):.3f}")
    print(f"RF test accuracy: {rf.score(X_test, y_test):.3f}")


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.. code-block:: Python

    train_result = permutation_importance(
        rf, X_train, y_train, n_repeats=10, random_state=42, n_jobs=2
    )
    test_results = permutation_importance(
        rf, X_test, y_test, n_repeats=10, random_state=42, n_jobs=2
    )
    sorted_importances_idx = train_result.importances_mean.argsort()


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.. code-block:: Python

    train_importances = pd.DataFrame(
        train_result.importances[sorted_importances_idx].T,
        columns=X.columns[sorted_importances_idx],
    )
    test_importances = pd.DataFrame(
        test_results.importances[sorted_importances_idx].T,
        columns=X.columns[sorted_importances_idx],
    )


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.. code-block:: Python

    for name, importances in zip(["train", "test"], [train_importances, test_importances]):
        ax = importances.plot.box(vert=False, whis=10)
        ax.set_title(f"Permutation Importances ({name} set)")
        ax.set_xlabel("Decrease in accuracy score")
        ax.axvline(x=0, color="k", linestyle="--")
        ax.figure.tight_layout()


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Now, we can observe that on both sets, the `random_num` and `random_cat`
features have a lower importance compared to the overfitting random forest.
However, the conclusions regarding the importance of the other features are
still valid.


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.002 seconds)


.. _sphx_glr_download_auto_examples_inspection_plot_permutation_importance.py:

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      :download:`Download Python source code: plot_permutation_importance.py <plot_permutation_importance.py>`

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