Configure SGDRegressor "penalty" Parameter

The penalty parameter in scikit-learn’s SGDRegressor controls the type of regularization applied to the model during training.

Stochastic Gradient Descent (SGD) is an optimization method used for fitting linear models. The SGDRegressor implements regularized linear regression models trained using SGD.

The penalty parameter determines the type of regularization used to prevent overfitting. It can be set to ’l2’ (L2 regularization), ’l1’ (L1 regularization), ’elasticnet’ (combination of L1 and L2), or None (no regularization).

The default value for penalty is ’l2’. Common choices include ’l2’ for general-purpose regularization, ’l1’ for feature selection, and ’elasticnet’ for a balance between the two.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split
from sklearn.linear_model import SGDRegressor
from sklearn.metrics import mean_squared_error
import numpy as np

# Generate synthetic dataset
X, y = make_regression(n_samples=1000, n_features=20, noise=0.1, random_state=42)

# Split into train and test sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Train with different penalty values
penalties = ['l2', 'l1', 'elasticnet', None]
mse_scores = []

for penalty in penalties:
    sgd = SGDRegressor(penalty=penalty, random_state=42)
    sgd.fit(X_train, y_train)
    y_pred = sgd.predict(X_test)
    mse = mean_squared_error(y_test, y_pred)
    mse_scores.append(mse)
    print(f"penalty={penalty}, Mean Squared Error: {mse:.3f}")

# Find best penalty
best_penalty = penalties[np.argmin(mse_scores)]
print(f"Best penalty: {best_penalty}")

Running the example gives an output like:

penalty=l2, Mean Squared Error: 0.012
penalty=l1, Mean Squared Error: 0.011
penalty=elasticnet, Mean Squared Error: 0.012
penalty=None, Mean Squared Error: 0.011
Best penalty: l1

The key steps in this example are:

Generate a synthetic regression dataset
Split the data into train and test sets
Train SGDRegressor models with different penalty values
Evaluate the mean squared error of each model on the test set
Identify the best performing penalty type

Tips for choosing the appropriate penalty type:

Use ’l2’ for general-purpose regularization and to prevent large coefficient values
Choose ’l1’ for feature selection, as it promotes sparsity in the coefficient values
Opt for ’elasticnet’ to combine the benefits of both L1 and L2 regularization
Use None when you want to disable regularization entirely

Considerations when using different penalties:

L2 penalty tends to shrink all coefficients towards zero, but not exactly to zero
L1 penalty can set some coefficients exactly to zero, effectively performing feature selection
Elasticnet combines L1 and L2 penalties, offering a balance between feature selection and coefficient shrinkage
The strength of the regularization is controlled by the alpha parameter, which should be tuned in conjunction with the penalty type

See Also