RecursiveFeatureElimination#

RecursiveFeatureElimination implements recursive feature elimination. Recursive feature elimination (RFE) is a backward feature selection process.

In Feature-engine’s implementation of RFE, a feature will be kept or removed based on the resulting change in model performance resulting of adding that feature to a machine learning. This differs from Scikit-learn’s implementation of RFE where a feature will be kept or removed based on the feature importance derived from a machine learning model via it’s coefficients parameters or ‘feature_importances_` attribute.

Feature-engine’s implementation of RFE begins by training a model on the entire set of variables, and storing its performance value. From this same model, RecursiveFeatureElimination derives the feature importance through the coef_ or feature_importances_ attributes, depending if it is a linear model or a tree-based algorithm. These feature importance value is used to sort the features by incraeasing performance, to determine the order in which the features will be recursively removed. The least important features are removed first.

In the next step, RecursiveFeatureElimination removes the least important feature and trains a new machine learning model using the remaining variables. If the performance of this model is worse than the performance from the previus model, then, the feature is kept (because eliminating the feature caused a drop in model performance) otherwise, it removed.

RecursiveFeatureElimination removes now the second least important feature, trains a new model, compares its performance to the previous model, determines if it should remove or retain the feature, and moves on to the next variable until it evaluates all the features in the dataset.

Note that, in Feature-engine’s implementation of RFE, the feature importance is used just to rank features and thus determine the order in which the features will be eliminated. But whether to retain a feature is determined based on the decrease in the performance of the model after the feature elimination.

By recursively eliminating features, RFE attempts to eliminate dependencies and collinearity that may exist in the model.

Parameters#

RecursiveFeatureElimination has 2 parameters that need to be determined somewhat arbitrarily by the user: the first one is the machine learning model which performance will be evaluated. The second is the threshold in the performance drop that needs to occur to remove a feature.

RFE is not machine learning model agnostic, this means that the feature selection depends on the model, and different models may have different subsets of optimal features. Thus, it is recommended that you use the machine learning model that you finally intend to build.

Regarding the threshold, this parameter needs a bit of hand tuning. Higher thresholds will return fewer features.

Python example#

Let’s see how to use this transformer with the diabetes dataset that comes in Scikit-learn. First, we load the data:

import matplotlib.pyplot as plt
import pandas as pd
from sklearn.datasets import load_diabetes
from sklearn.linear_model import LinearRegression
from feature_engine.selection import RecursiveFeatureElimination

# load dataset
X, y = load_diabetes(return_X_y=True, as_frame=True)

print(X.head())

In the following output we see the diabetes dataset:

        age       sex       bmi        bp        s1        s2        s3  \
0  0.038076  0.050680  0.061696  0.021872 -0.044223 -0.034821 -0.043401
1 -0.001882 -0.044642 -0.051474 -0.026328 -0.008449 -0.019163  0.074412
2  0.085299  0.050680  0.044451 -0.005670 -0.045599 -0.034194 -0.032356
3 -0.089063 -0.044642 -0.011595 -0.036656  0.012191  0.024991 -0.036038
4  0.005383 -0.044642 -0.036385  0.021872  0.003935  0.015596  0.008142

         s4        s5        s6
0 -0.002592  0.019907 -0.017646
1 -0.039493 -0.068332 -0.092204
2 -0.002592  0.002861 -0.025930
3  0.034309  0.022688 -0.009362
4 -0.002592 -0.031988 -0.046641

Now, we set up RecursiveFeatureElimination to select features based on the r2 returned by a Linear Regression model, using 3 fold cross-validation. In this case, we leave the parameter threshold to the default value which is 0.01.

# initialize linear regresion estimator
linear_model = LinearRegression()

# initialize feature selector
tr = RecursiveFeatureElimination(estimator=linear_model, scoring="r2", cv=3)

With fit() the model finds the most useful features, that is, features that when removed cause a drop in model performance bigger than 0.01. With transform(), the transformer removes the features from the dataset.

Xt = tr.fit_transform(X, y)
print(Xt.head())

Six features were deemed important by recursive feature elimination with linear regression:

        sex       bmi        bp        s1        s2        s5
0  0.050680  0.061696  0.021872 -0.044223 -0.034821  0.019907
1 -0.044642 -0.051474 -0.026328 -0.008449 -0.019163 -0.068332
2  0.050680  0.044451 -0.005670 -0.045599 -0.034194  0.002861
3 -0.044642 -0.011595 -0.036656  0.012191  0.024991  0.022688
4 -0.044642 -0.036385  0.021872  0.003935  0.015596 -0.031988

RecursiveFeatureElimination stores the performance of the model trained using all the features in its attribute:

# get the initial linear model performance, using all features
tr.initial_model_performance_

In the following output we see the performance of the linear regression trained on the entire dataset:

0.488702767247119

Evaluating feature importance#

The coefficients of the linear regression are used to determine the initial feature importance score, which is used to sort the features before applying the recursive elimination process. We can check out the feature importance as follows:

tr.feature_importances_

In the following output we see the feature importance derived from the linear model:

age     41.418041
s6      64.768417
s3     113.965992
s4     182.174834
sex    238.619526
bp     322.091802
s2     436.671584
bmi    522.330165
s5     741.471337
s1     750.023872
dtype: float64

The feature importance is obtained using cross-validation, so RecursiveFeatureElimination also stores the standard deviation of the feature importance:

tr.feature_importances_std_

In the following output we see the standard deviation of the feature importance:

age     18.217152
sex     68.354719
bmi     86.030698
bp      57.110383
s1     329.375819
s2     299.756998
s3      72.805496
s4      47.925822
s5     117.829949
s6      42.754774
dtype: float64

The selection procedure is based on whether removing a feature decreases the performance of a model compared to the same model with that feature. We can check out the performance changes as follows:

# Get the performance drift of each feature
tr.performance_drifts_

In the following output we see the changes in performance returned by removing each feature:

{'age': -0.0032800993162502845,
 's6': -0.00028194870232089997,
 's3': -0.0006751427734088544,
 's4': 0.00013890056776355575,
 'sex': 0.01195652626644067,
 'bp': 0.02863360798239445,
 's2': 0.012639242239088355,
 'bmi': 0.06630359039334816,
 's5': 0.10937354113435072,
 's1': 0.024318355833473526}

We can also check out the standard deviation of the performance drift:

# Get the performance drift of each feature
tr.performance_drifts_std_

In the following output we see the standard deviation of the changes in performance returned by eliminating each feature:

{'age': 0.013642261032787014,
 's6': 0.01678934235354838,
 's3': 0.01685859860738229,
 's4': 0.017977817100713972,
 'sex': 0.025202392033518706,
 'bp': 0.00841776123355417,
 's2': 0.008676750772593812,
 'bmi': 0.042463565656018436,
 's5': 0.046779680487815146,
 's1': 0.01621466049786452}

We can now plot the performance change with the standard deviation to identify importance features:

r = pd.concat([
    pd.Series(tr.performance_drifts_),
    pd.Series(tr.performance_drifts_std_)
], axis=1
)
r.columns = ['mean', 'std']

r['mean'].plot.bar(yerr=[r['std'], r['std']], subplots=True)

plt.title("Performance drift elicited by adding features")
plt.ylabel('Mean performance drift')
plt.xlabel('Features')
plt.show()

In the following image we see the change in performance resulting from removing each feature from a model:

../../_images/rfe_perf_drift.png

For comparison, we can plot the feature importance derived from the linear regression together with the standard deviation:

r = pd.concat([
    tr.feature_importances_,
    tr.feature_importances_std_,
], axis=1
)
r.columns = ['mean', 'std']

r['mean'].plot.bar(yerr=[r['std'], r['std']], subplots=True)

plt.title("Feature importance derived from the linear regression")
plt.ylabel('Coefficients value')
plt.xlabel('Features')
plt.show()

In the following image we see the feature importance determined by the coefficients of the linear regression:

../../_images/rfa_linreg_imp.png

By comparing the performance in both plots, we can begin to understand which features are important, and which ones could show some correlation to other variables in the data. If a feature has a relatively big coefficient, but removing it does not change the model performance, then, it might be correlated to another variable in the data.

Checking out the eliminated features#

RecursiveFeatureElimination also stores the features that will be dropped based on the given threshold.

# the features to remove
tr.features_to_drop_

These features were not deemed important by the RFE process:

['age', 's3', 's4', 's6']

RecursiveFeatureElimination also has the get_support() method that works exactly like that of Scikit-learn’s feature selection classes:

tr.get_support()

The output contains True for the features that are selected and False for those that will be dropped:

[False, True, True, True, True, True, False, False, True, False]

And that’s it! You now now how to select features by recursively removing them to a dataset.

Additional resources#

More details on recursive feature elimination in this article:

For more details about this and other feature selection methods check out these resources:

For more details about this and other feature selection methods check out these resources:

../../_images/fsml.png

Feature Selection for Machine Learning#











Or read our book:

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Feature Selection in Machine Learning#















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