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        Click :ref:`here <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.

.. topic:: References:

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

.. GENERATED FROM PYTHON SOURCE LINES 29-41

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).

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.. code-block:: default

    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/scikit-learn-Ye5PqW/scikit-learn-1.4.1.post1+dfsg/examples/inspection/plot_permutation_importance.py", line 46, in <module>
        X, y = fetch_openml("titanic", version=1, as_frame=True, return_X_y=True)
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
      File "/build/scikit-learn-Ye5PqW/scikit-learn-1.4.1.post1+dfsg/.pybuild/cpython3_3.12/build/sklearn/utils/_param_validation.py", line 213, in wrapper
        return func(*args, **kwargs)
               ^^^^^^^^^^^^^^^^^^^^^
      File "/build/scikit-learn-Ye5PqW/scikit-learn-1.4.1.post1+dfsg/.pybuild/cpython3_3.12/build/sklearn/datasets/_openml.py", line 992, 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




.. GENERATED FROM PYTHON SOURCE LINES 58-65

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.

.. GENERATED FROM PYTHON SOURCE LINES 65-92

.. code-block:: default

    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 93-113

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

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's keep our high capacity random forest model for now so as to
illustrate some pitfalls with feature importance on variables with many
unique values.

.. GENERATED FROM PYTHON SOURCE LINES 113-117

.. code-block:: default

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



.. GENERATED FROM PYTHON SOURCE LINES 118-139

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 both random features to 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.

.. GENERATED FROM PYTHON SOURCE LINES 139-147

.. code-block:: default

    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)


.. GENERATED FROM PYTHON SOURCE LINES 148-152

.. code-block:: default

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


.. GENERATED FROM PYTHON SOURCE LINES 153-161

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 feature. Indeed, permuting the
values of these features will lead to 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.

.. GENERATED FROM PYTHON SOURCE LINES 161-178

.. code-block:: default

    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 179-184

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 184-199

.. code-block:: default

    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()


.. GENERATED FROM PYTHON SOURCE LINES 200-202

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

.. GENERATED FROM PYTHON SOURCE LINES 202-204

.. code-block:: default

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


.. GENERATED FROM PYTHON SOURCE LINES 205-208

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 208-211

.. code-block:: default

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


.. GENERATED FROM PYTHON SOURCE LINES 212-220

.. code-block:: default

    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()


.. GENERATED FROM PYTHON SOURCE LINES 221-230

.. code-block:: default

    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],
    )


.. GENERATED FROM PYTHON SOURCE LINES 231-238

.. code-block:: default

    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()


.. GENERATED FROM PYTHON SOURCE LINES 239-243

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.


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