Implementation:Scikit learn Scikit learn Ridge

Knowledge Sources	Scikit_learn Scikit-learn Docs
Domains	Machine Learning, Regularized Regression
Last Updated	2026-02-08 15:00 GMT

Overview

Concrete tool for linear least squares regression with L2 regularization (Tikhonov regularization) provided by scikit-learn.

Description

Ridge implements linear least squares with L2 regularization, minimizing ||y - Xw||^2_2 + alpha * ||w||^2_2. Also known as Ridge Regression or Tikhonov regularization, it addresses multicollinearity and overfitting by shrinking coefficient magnitudes. The implementation supports multiple solvers including SVD decomposition, Cholesky factorization, sparse conjugate gradient, LSQR, SAG/SAGA, and L-BFGS. It natively supports multi-variate regression (2d target arrays) and per-target regularization strengths. The module also includes RidgeClassifier for classification tasks.

Usage

Use Ridge when you have correlated features (multicollinearity), when ordinary least squares overfits, or when you want to regularize a linear model without inducing sparsity. It is particularly useful when all features are believed to be relevant but their individual contributions should be dampened. Ridge is often preferred over Lasso when you do not expect a sparse solution.

Code Reference

Source Location

• Repository: scikit-learn
• File: sklearn/linear_model/_ridge.py

Signature

class Ridge(MultiOutputMixin, RegressorMixin, _BaseRidge):
    def __init__(
        self,
        alpha=1.0,
        *,
        fit_intercept=True,
        copy_X=True,
        max_iter=None,
        tol=1e-4,
        solver="auto",
        positive=False,
        random_state=None,
    ):

Import

from sklearn.linear_model import Ridge

I/O Contract

Inputs

Name	Type	Required	Description
alpha	float or ndarray of shape (n_targets,)	No	L2 regularization strength; must be non-negative (default=1.0)
fit_intercept	bool	No	Whether to fit the intercept (default=True)
copy_X	bool	No	Whether to copy X (default=True)
max_iter	int	No	Maximum iterations for iterative solvers (default=None, solver-dependent)
tol	float	No	Precision of the solution for iterative solvers (default=1e-4)
solver	str	No	Solver: 'auto', 'svd', 'cholesky', 'lsqr', 'sparse_cg', 'sag', 'saga', 'lbfgs' (default='auto')
positive	bool	No	Force coefficients to be positive (default=False)
random_state	int or RandomState	No	Random seed for 'sag' and 'saga' solvers

Outputs

Name	Type	Description
coef_	ndarray of shape (n_features,) or (n_targets, n_features)	Estimated weight vector
intercept_	float or ndarray of shape (n_targets,)	Independent term in the linear model
n_iter_	int or None	Number of iterations for iterative solvers

Usage Examples

Basic Usage

from sklearn.linear_model import Ridge
from sklearn.datasets import make_regression

X, y = make_regression(n_samples=100, n_features=20, noise=10, random_state=42)
model = Ridge(alpha=1.0)
model.fit(X, y)
print("Score:", model.score(X, y))
print("Intercept:", model.intercept_)

Related Pages

• Principle:Scikit_learn_Scikit_learn_Linear_Regression