Does scikit-learn have a forward selection/stepwise regression algorithm?

Question

I am working on a problem with too many features and training my models takes way too long. I implemented a forward selection algorithm to choose features.

However, I was wondering does scikit-learn have a forward selection/stepwise regression algorithm?

Answer 1

No, scikit-learn does not seem to have a forward selection algorithm. However, it does provide recursive feature elimination, which is a greedy feature elimination algorithm similar to sequential backward selection. See the documentation here

Answer 2

Scikit-learn indeed does not support stepwise regression. That's because what is commonly known as 'stepwise regression' is an algorithm based on p-values of coefficients of linear regression, and scikit-learn deliberately avoids inferential approach to model learning (significance testing etc). Moreover, pure OLS is only one of numerous regression algorithms, and from the scikit-learn point of view it is neither very important, nor one of the best.

There are, however, some pieces of advice for those who still need a good way for feature selection with linear models:

1. Use inherently sparse models like ElasticNet or Lasso.
2. Normalize your features with StandardScaler, and then order your features just by model.coef_. For perfectly independent covariates it is equivalent to sorting by p-values. The class sklearn.feature_selection.RFE will do it for you, and RFECV will even evaluate the optimal number of features.
3. Use [an implementation][1] of forward selection by adjusted $R^2$ that works with statsmodels.
4. Do brute-force forward or backward selection to maximize your favorite metric on cross-validation (it could take approximately quadratic time in number of covariates). A scikit-learn compatible mlxtend package [supports][2] this approach for any estimator and any metric.
5. If you still want vanilla stepwise regression, it is easier to base it on statsmodels, since this package calculates p-values for you. A basic forward-backward selection could look like this:

    from sklearn.datasets import load_boston
    import pandas as pd
    import numpy as np
    import statsmodels.api as sm

    data = load_boston()
    X = pd.DataFrame(data.data, columns=data.feature_names)
    y = data.target


    def stepwise_selection(X, y, 
                           initial_list=[], 
                           threshold_in=0.01, 
                           threshold_out = 0.05, 
                           verbose=True):
        """ Perform a forward-backward feature selection 
        based on p-value from statsmodels.api.OLS
        Arguments:
            X - pandas.DataFrame with candidate features
            y - list-like with the target
            initial_list - list of features to start with (column names of X)
            threshold_in - include a feature if its p-value < threshold_in
            threshold_out - exclude a feature if its p-value > threshold_out
            verbose - whether to print the sequence of inclusions and exclusions
        Returns: list of selected features 
        Always set threshold_in < threshold_out to avoid infinite looping.
        See https://en.wikipedia.org/wiki/Stepwise_regression for the details
        """
        included = list(initial_list)
        while True:
            changed=False
            # forward step
            excluded = list(set(X.columns)-set(included))
            new_pval = pd.Series(index=excluded)
            for new_column in excluded:
                model = sm.OLS(y, sm.add_constant(pd.DataFrame(X[included+[new_column]]))).fit()
                new_pval[new_column] = model.pvalues[new_column]
            best_pval = new_pval.min()
            if best_pval < threshold_in:
                best_feature = new_pval.idxmin()
                included.append(best_feature)
                changed=True
                if verbose:
                    print('Add  {:30} with p-value {:.6}'.format(best_feature, best_pval))

            # backward step
            model = sm.OLS(y, sm.add_constant(pd.DataFrame(X[included]))).fit()
            # use all coefs except intercept
            pvalues = model.pvalues.iloc[1:]
            worst_pval = pvalues.max() # null if pvalues is empty
            if worst_pval > threshold_out:
                changed=True
                worst_feature = pvalues.idxmax()
                included.remove(worst_feature)
                if verbose:
                    print('Drop {:30} with p-value {:.6}'.format(worst_feature, worst_pval))
            if not changed:
                break
        return included

    result = stepwise_selection(X, y)

    print('resulting features:')
    print(result)


This example would print the following output:

    Add  LSTAT                          with p-value 5.0811e-88
    Add  RM                             with p-value 3.47226e-27
    Add  PTRATIO                        with p-value 1.64466e-14
    Add  DIS                            with p-value 1.66847e-05
    Add  NOX                            with p-value 5.48815e-08
    Add  CHAS                           with p-value 0.000265473
    Add  B                              with p-value 0.000771946
    Add  ZN                             with p-value 0.00465162
    resulting features:
    ['LSTAT', 'RM', 'PTRATIO', 'DIS', 'NOX', 'CHAS', 'B', 'ZN']


  [1]: http://planspace.org/20150423-forward_selection_with_statsmodels/
  [2]: http://rasbt.github.io/mlxtend/user_guide/feature_selection/SequentialFeatureSelector/

Answer 3

Sklearn DOES have a forward selection algorithm, although it isn't called that in scikit-learn. The feature selection method called F_regression in scikit-learn will sequentially include features that improve the model the most, until there are K features in the model (K is an input).

It starts by regression the labels on each feature individually, and then observing which feature improved the model the most using the F-statistic. Then it incorporates the winning feature into the model. Then it iterates through the remaining features to find the next feature which improves the model the most, again using the F-statistic or F test. It does this until there are K features in the model.

Notice that the remaining features that are correlated to features incorporated into the model will probably not be selected, since they do not correlate with the residuals (although they might correlate well with the labels). This helps guard against multi-collinearity.

Answer 4

As of version 0.24, it does!

Announcement, documentation

Answer 5

In fact there is a nice algorithm called "Forward_Select" that uses Statsmodels and allows you to set your own metric (AIC, BIC, Adjusted-R-Squared, or whatever you like) to progressively add a variable to the model. The algorithm can be found in the comments section of this page - scroll down and you'll see it near the bottom of the page.

https://planspace.org/20150423-forward_selection_with_statsmodels/

I would add that the algorithm also has one nice feature: you can apply it to either classification or regression problems! You just have to tell it.

Try it and see for yourself.

Answer 6

Actually sklearn doesn't have a forward selection algorithm, thought a pull request with an implementation of forward feature selection waits in the Scikit-Learn repository since April 2017.

As an alternative, there is forward and one-step-ahead backward selection in mlxtend. You can find it's document in Sequential Feature Selector

Answer 7

I developed this repository link. My Stepwise Selection Classes (best subset, forward stepwise, backward stepwise) are compatible to sklearn. You can do Pipeline and GridSearchCV with my Classes.

Answer 8

Yes

sklearn.feature_selection.SequentialFeatureSelector

https://scikit-learn.org/0.24/modules/generated/sklearn.feature_selection.SequentialFeatureSelector.html

also

http://rasbt.github.io/mlxtend/user_guide/feature_selection/SequentialFeatureSelector/

from sklearn.linear_model import LinearRegression
from sklearn.datasets import load_boston

boston = load_boston()
X, y = boston.data, boston.target

lr = LinearRegression()

sfs = SFS(lr, 
          k_features=13, 
          forward=True, 
          floating=False, 
          scoring='neg_mean_squared_error',
          cv=10)

sfs = sfs.fit(X, y)
fig = plot_sfs(sfs.get_metric_dict(), kind='std_err')

plt.title('Sequential Forward Selection (w. StdErr)')
plt.grid()
plt.show()