Implementation:Scikit learn Scikit learn KernelRidge

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

Overview

Concrete tool for performing kernel ridge regression combining ridge regression with the kernel trick, provided by scikit-learn.

Description

The KernelRidge class combines ridge regression (linear least squares with L2-norm regularization) with the kernel trick. It learns a linear function in the kernel-induced feature space, which corresponds to a non-linear function in the original space for non-linear kernels. Unlike SVR, KRR uses squared error loss and can be solved in closed form. It supports multi-variate regression when y is a 2D array.

Usage

Use this estimator when you need non-linear regression with a closed-form solution. It is typically faster than SVR for medium-sized datasets but produces a non-sparse model, making it slower at prediction time.

Code Reference

Source Location

• Repository: scikit-learn
• File: sklearn/kernel_ridge.py

Signature

class KernelRidge(MultiOutputMixin, RegressorMixin, BaseEstimator):
    def __init__(
        self,
        alpha=1.0,
        *,
        kernel="linear",
        gamma=None,
        degree=3,
        coef0=1,
    ):

Import

from sklearn.kernel_ridge import KernelRidge

I/O Contract

Inputs

Name	Type	Required	Description
alpha	float or array-like	No	Regularization strength (default 1.0)
kernel	str or callable	No	Kernel mapping: 'linear', 'poly', 'rbf', etc. (default 'linear')
gamma	float or None	No	Kernel coefficient for rbf, laplacian, polynomial, sigmoid (default None)
degree	int	No	Degree of the polynomial kernel (default 3)
coef0	float	No	Independent term in polynomial and sigmoid kernels (default 1)

Outputs

Name	Type	Description
dual_coef_	ndarray of shape (n_samples,) or (n_samples, n_targets)	Representation of weight vector in kernel space
X_fit_	ndarray of shape (n_samples, n_features)	Training data used in fitting

Usage Examples

Basic Usage

from sklearn.kernel_ridge import KernelRidge
import numpy as np

X = np.array([[1, 1], [2, 2], [3, 3]])
y = np.array([1, 2, 3])
krr = KernelRidge(alpha=1.0, kernel="rbf", gamma=0.1)
krr.fit(X, y)
print(krr.predict([[1.5, 1.5]]))

Related Pages

• Principle:Scikit_learn_Scikit_learn_Linear_Regression