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:
- Use inherently sparse models like
ElasticNet
or Lasso
.
- 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.
- Use [an implementation][1] of forward selection by adjusted $R^2$ that works with
statsmodels
.
- 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.
- 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/