Implementation:Scikit learn Scikit learn GPKernels

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

Overview

Concrete implementations of kernel functions for Gaussian process regression and classification provided by scikit-learn.

Description

The kernels module provides a rich set of kernel functions that can be combined via "+" and "*" operators or exponentiated with "**". The abstract Kernel base class defines the interface. Key kernels include RBF (squared exponential), Matern, ConstantKernel, WhiteKernel, DotProduct, RationalQuadratic, and ExpSineSquared. All kernels support analytic gradient-based hyperparameter optimization via the Hyperparameter namedtuple.

Usage

Use these kernels when configuring Gaussian process models. Combine kernels to model complex covariance structures (e.g., periodic + smooth trends). Hyperparameters are automatically optimized during GP fitting unless their bounds are set to "fixed".

Code Reference

Source Location

• Repository: scikit-learn
• File: sklearn/gaussian_process/kernels.py

Signature

class Hyperparameter(namedtuple("Hyperparameter",
    ("name", "value_type", "bounds", "n_elements", "fixed"))):
    ...

class Kernel(metaclass=ABCMeta):
    def __call__(self, X, Y=None, eval_gradient=False):
        ...
    def __add__(self, b):
        ...
    def __mul__(self, b):
        ...
    def __pow__(self, b):
        ...

class ConstantKernel(StationaryKernelMixin, GenericKernelMixin, Kernel):
    def __init__(self, constant_value=1.0, constant_value_bounds=(1e-5, 1e5)):
        ...

class RBF(StationaryKernelMixin, NormalizedKernelMixin, Kernel):
    def __init__(self, length_scale=1.0, length_scale_bounds=(1e-5, 1e5)):
        ...

class Matern(RBF):
    def __init__(self, length_scale=1.0, length_scale_bounds=(1e-5, 1e5), nu=1.5):
        ...

class WhiteKernel(StationaryKernelMixin, GenericKernelMixin, Kernel):
    def __init__(self, noise_level=1.0, noise_level_bounds=(1e-5, 1e5)):
        ...

class DotProduct(Kernel):
    def __init__(self, sigma_0=1.0, sigma_0_bounds=(1e-5, 1e5)):
        ...

Import

from sklearn.gaussian_process.kernels import (
    RBF, Matern, ConstantKernel, WhiteKernel, DotProduct, Kernel
)

I/O Contract

Inputs

Name	Type	Required	Description
X	array-like of shape (n_samples_X, n_features)	Yes	Left argument of the kernel
Y	array-like of shape (n_samples_Y, n_features)	No	Right argument (if None, K(X, X) is computed)
eval_gradient	bool	No	Whether to return gradient w.r.t. kernel hyperparameters
length_scale	float or ndarray	No	Length scale parameter (for RBF, Matern)
nu	float	No	Smoothness parameter for Matern kernel

Outputs

Name	Type	Description
K	ndarray of shape (n_samples_X, n_samples_Y)	Kernel matrix
K_gradient	ndarray of shape (n_samples_X, n_samples_X, n_dims)	Gradient of kernel matrix (if eval_gradient=True)

Usage Examples

Basic Usage

import numpy as np
from sklearn.gaussian_process.kernels import RBF, ConstantKernel as C, WhiteKernel

# Compose a kernel: constant * RBF + noise
kernel = C(1.0) * RBF(length_scale=1.0) + WhiteKernel(noise_level=0.1)
print(kernel)  # 1**2 * RBF(length_scale=1) + WhiteKernel(noise_level=0.1)

# Evaluate kernel matrix
X = np.array([[0], [1], [2]])
K = kernel(X)
print(K.shape)  # (3, 3)

Related Pages

• Principle:Scikit_learn_Scikit_learn_Kernel_Methods