Backward Stepwise Feature Selection With Scikit-Learn

This tutorial explains how to use feature importance from scikit-learn to perform backward stepwise feature selection. The feature importance used is the gini importance from a tree based model.

This will prune the features to model arrival delay for flights in and out of NYC in 2013.


import statsmodels.api as sm
import pandas as pd
import numpy as np
from sklearn.metrics import mean_squared_error
from sklearn.model_selection import train_test_split
import category_encoders as ce

from sklearn.ensemble import GradientBoostingRegressor

Reading the Data

The data is from rdatasets imported using the Python package statsmodels.


df = sm.datasets.get_rdataset('flights', 'nycflights13').data
df.info()

This should return a table resembling something like this:



RangeIndex: 336776 entries, 0 to 336775
Data columns (total 19 columns):
 #   Column          Non-Null Count   Dtype  
---  ------          --------------   -----  
 0   year            336776 non-null  int64  
 1   month           336776 non-null  int64  
 2   day             336776 non-null  int64  
 3   dep_time        328521 non-null  float64
 4   sched_dep_time  336776 non-null  int64  
 5   dep_delay       328521 non-null  float64
 6   arr_time        328063 non-null  float64
 7   sched_arr_time  336776 non-null  int64  
 8   arr_delay       327346 non-null  float64
 9   carrier         336776 non-null  object 
 10  flight          336776 non-null  int64  
 11  tailnum         334264 non-null  object 
 12  origin          336776 non-null  object 
 13  dest            336776 non-null  object 
 14  air_time        327346 non-null  float64
 15  distance        336776 non-null  int64  
 16  hour            336776 non-null  int64  
 17  minute          336776 non-null  int64  
 18  time_hour       336776 non-null  object 
dtypes: float64(5), int64(9), object(5)
memory usage: 48.8+ MB

Feature Engineering

Handle Null Values

As this model will predict arrival delay, the Null values are caused by flights did were cancelled or diverted. These can be excluded from this analysis.


df.dropna(inplace=True)

Convert the Times From Floats or Ints to Hour and Minutes


df['arr_hour'] = df.arr_time.apply(lambda x: int(np.floor(x/100)))
df['arr_minute'] = df.arr_time.apply(lambda x: int(x - np.floor(x/100)*100))
df['sched_arr_hour'] = df.sched_arr_time.apply(lambda x: int(np.floor(x/100)))
df['sched_arr_minute'] = df.sched_arr_time.apply(lambda x: int(x - np.floor(x/100)*100))
df['sched_dep_hour'] = df.sched_dep_time.apply(lambda x: int(np.floor(x/100)))
df['sched_dep_minute'] = df.sched_dep_time.apply(lambda x: int(x - np.floor(x/100)*100))
df.rename(columns={'hour': 'dep_hour',
                   'minute': 'dep_minute'}, inplace=True)

Feature Selection

Define Function

Function to build the model.


def build_model(df, target):
    """
    Given the dataframe and target, build and return the model
    """
    # Set up target
    y = df[target]
    # Set up train-test split
    X = df.drop(columns=[target])
    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=.2, random_state=1066)
    # Encode the categorical variables
    encoder = ce.LeaveOneOutEncoder(return_df=True)
    X_train_loo = encoder.fit_transform(X_train, y_train)
    X_test_loo = encoder.transform(X_test)
    # Fit the model and calculate RMSE
    # NOTE: You really should do some hyperparameter tuning here. 
    model = GradientBoostingRegressor(learning_rate=0.05, max_depth=5, n_estimators=500, min_samples_split=5, n_iter_no_change=10)
    model.fit(X_train_loo, y_train)
    rmse = np.sqrt(mean_squared_error(y_test, model.predict(X_test_loo)))
    return rmse, model, X_train_loo.columns

Function to return feature to be dropped


def get_dropped_feature(model, features):
    feature_importance = model.feature_importances_
    importance_df = pd.DataFrame({'features': features,
                                  'importance': feature_importance})
    importance_df.sort_values(by='importance', ascending=False, inplace=True)
    return importance_df['features'].iloc[-1]

Function that incremental removes the feature with the lowest feature importance as calculated by scikit-learn until the RMSE stops decreasing.


def backward_selection(df, target, max_features=None):

This function uses gini importance from a sklearn GBM model to incrementally remove features from the training set until the RMSE no longer improves.

This function returns the dataframe with the features that give the best RMSE. Return at most max_features.

# get baseline RMSE
select_df = df.copy()
total_features = df.shape[1]
rmse, model, features = build_model(select_df, target)
print(f"{rmse} with {select_df.shape[1]}")
last_rmse = rmse

# Drop least important feature and recalculate model peformanceif max_features isNone:

max_features = total_features-1

for num_features in range(total_features-1, 0, -1):# Trim features

dropped_feature = get_dropped_feature(model, features)
tmp_df = select_df.drop(columns=[dropped_feature])

# Rerun modeling
rmse, model, features = build_model(tmp_df, target)
print(f"{rmse} with {tmp_df.shape[1]}")if (num_features < max_features) and (rmse > last_rmse):# RMSE increased, return last dataframe

return select_dfelse:# RMSE improved, continue dropping features

last_rmse = rmse
select_df = tmp_dfreturn select_df

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Run stepwise feature selection

Call backward_selection on the modeling dataframe. reduced_df will contain the selected features and will be our reduced modeling dataset.


target = 'arr_delay'
reduced_df = backward_selection(df, target, max_features=20)
reduced_df.shape[1]

30.54691197243769 with 25
30.479507645969033 with 24
30.35605963373274 with 23
30.702390669186062 with 22
30.79658581770791 with 21
29.975162972788738 with 20
30.5938801236653 with 19

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