Configure SGDRegressor "l1_ratio" Parameter

The l1_ratio parameter in scikit-learn’s SGDRegressor controls the balance between L1 and L2 regularization.

SGDRegressor uses elastic net regularization, which combines L1 and L2 penalties. The l1_ratio parameter determines the mix of these penalties, allowing for fine-tuned regularization.

l1_ratio ranges from 0 to 1. A value of 0 corresponds to L2 regularization only, while 1 means pure L1 regularization. Values between 0 and 1 represent a mix of both.

The default value for l1_ratio is 0.15, which favors L2 regularization. Common values range from 0.1 to 0.9, depending on the desired balance between feature selection and model stability.

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
import matplotlib.pyplot as plt

# 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 l1_ratio values
l1_ratio_values = [0, 0.15, 0.5, 0.85, 1]
mse_scores = []

for ratio in l1_ratio_values:
    sgd = SGDRegressor(l1_ratio=ratio, 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"l1_ratio={ratio}, MSE: {mse:.3f}")

Running the example gives an output like:

l1_ratio=0, MSE: 0.012
l1_ratio=0.15, MSE: 0.012
l1_ratio=0.5, MSE: 0.012
l1_ratio=0.85, MSE: 0.012
l1_ratio=1, MSE: 0.012

The key steps in this example are:

Generate a synthetic regression dataset with multiple features
Split the data into train and test sets
Train SGDRegressor models with different l1_ratio values
Evaluate the mean squared error of each model on the test set

Some tips and heuristics for setting l1_ratio:

Start with the default value of 0.15 and adjust based on model performance
Use higher values (closer to 1) for sparse feature selection
Lower values (closer to 0) can improve stability for dense feature sets
Employ cross-validation to find the optimal value for your specific dataset

Issues to consider:

L1 regularization promotes sparsity, while L2 handles correlated features better
Higher l1_ratio values may improve model interpretability by reducing feature count
The optimal l1_ratio depends on the nature of your data and the problem complexity
Very low or high values may lead to underfitting or overfitting, respectively

See Also