Machine Learning - Forward Feature Construction

Forward Feature Construction is a feature selection method in machine learning where we start with an empty set of features and iteratively add the best performing feature at each step until the desired number of features is reached.

The goal of feature selection is to identify the most important features that are relevant for predicting the target variable, while ignoring the less important features that add noise to the model and may lead to overfitting.

The steps involved in Forward Feature Construction are as follows −

• Initialize an empty set of features.

• Set the maximum number of features to be selected.

• Iterate until the desired number of features is reached −

  • For each remaining feature that is not already in the set of selected features, fit a model with the selected features and the current feature, and evaluate its performance using a validation set.

  • Select the feature that leads to the best performance and add it to the set of selected features.

• Return the set of selected features as the optimal set for the model.

The key advantage of Forward Feature Construction is that it is computationally efficient and can be used for high-dimensional datasets. However, it may not always lead to the optimal set of features, especially if there are highly correlated features or non-linear relationships between the features and the target variable.

Example

Here is an example to implement Forward Feature Construction in Python −

# Importing the necessary libraries
import pandas as pd
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error

# Load the diabetes dataset
diabetes = pd.read_csv(r'C:\Users\Leekha\Desktop\diabetes.csv')

# Define the predictor variables (X) and the target variable (y)
X = diabetes.iloc[:, :-1].values
y = diabetes.iloc[:, -1].values

# Split the data into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 0)

# Create an empty set of features
selected_features = set()

# Set the maximum number of features to be selected
max_features = 8

# Iterate until the desired number of features is reached
while len(selected_features) < max_features:

   # Set the best feature and the best score to be 0
   best_feature = None
   best_score = 0
   
   # Iterate over all the remaining features
   for i in range(X_train.shape[1]):

      # Skip the feature if it's already selected
      if i in selected_features:
         continue
      
      # Select the current feature and fit a linear regression model
      X_train_selected = X_train[:, list(selected_features) + [i]]
      regressor = LinearRegression()
      regressor.fit(X_train_selected, y_train)
      
      # Compute the score on the testing set
      X_test_selected = X_test[:, list(selected_features) + [i]]
      score = regressor.score(X_test_selected, y_test)

      # Update the best feature and score if the current feature performs better
      if score > best_score:
         best_feature = i
         best_score = score

   # Add the best feature to the set of selected features
   selected_features.add(best_feature)
   
   # Print the selected features and the score
   print('Selected Features:', list(selected_features))
   print('Score:', best_score)

Output

On execution, it will produce the following output −

Selected Features: [1]
Score: 0.23530716168783583
Selected Features: [0, 1]
Score: 0.2923143573608237
Selected Features: [0, 1, 5]
Score: 0.3164103491569179
Selected Features: [0, 1, 5, 6]
Score: 0.3287368302427327
Selected Features: [0, 1, 2, 5, 6]
Score: 0.334586804842275
Selected Features: [0, 1, 2, 3, 5, 6]
Score: 0.3356264736550455
Selected Features: [0, 1, 2, 3, 4, 5, 6]
Score: 0.3313166516703744
Selected Features: [0, 1, 2, 3, 4, 5, 6, 7]
Score: 0.32230203252064216