Configure SGDRegressor "alpha" Parameter

The alpha parameter in scikit-learn’s SGDRegressor controls the strength of regularization applied to the model’s coefficients.

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

The alpha parameter determines the amount of regularization. Higher values of alpha increase regularization, which can help prevent overfitting but may lead to underfitting if set too high.

The default value for alpha is 0.0001. In practice, values are often tuned in the range of 1e-5 to 1.0, depending on the scale of the target variable and the complexity of the problem.

import numpy as np
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 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 alpha values
alpha_values = [1e-5, 1e-4, 1e-3, 1e-2, 1e-1, 1.0]
mse_scores = []

for alpha in alpha_values:
    sgd = SGDRegressor(alpha=alpha, random_state=42, max_iter=1000)
    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"alpha={alpha}, MSE: {mse:.3f}")

Running the example gives an output like:

alpha=1e-05, MSE: 0.011
alpha=0.0001, MSE: 0.012
alpha=0.001, MSE: 0.052
alpha=0.01, MSE: 4.037
alpha=0.1, MSE: 339.606
alpha=1.0, MSE: 9813.859

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 alpha values
Evaluate the mean squared error of each model on the test set
Visualize the relationship between alpha and model performance

Some tips and heuristics for setting alpha:

Start with the default value and adjust based on model performance
Use cross-validation to find the optimal alpha for your dataset
Consider the scale of your target variable when choosing alpha values

Issues to consider:

Too low alpha may lead to overfitting, especially with high-dimensional data
Too high alpha can cause underfitting, resulting in poor model performance
The optimal alpha depends on the noise level and complexity of your data
Different regularization types (L1, L2, Elastic Net) may require different alpha ranges

See Also