Implementation:Scikit learn Scikit learn GaussianProcessRegressor

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

Overview

Concrete implementation of Gaussian Process Regression (GPR) provided by scikit-learn.

Description

The GaussianProcessRegressor implements Gaussian process regression based on Algorithm 2.1 of Rasmussen and Williams (2006). It provides predictions with uncertainty estimates (standard deviations), allows sampling from the posterior distribution via sample_y, and exposes log_marginal_likelihood for external hyperparameter selection. It supports prediction without prior fitting (using the GP prior) and multi-output regression.

Usage

Use Gaussian Process Regression when you need predictions with uncertainty estimates, particularly for small to medium datasets. GPR is well-suited for Bayesian optimization, surrogate modeling, and scenarios where quantifying prediction uncertainty is important.

Code Reference

Source Location

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

Signature

class GaussianProcessRegressor(MultiOutputMixin, RegressorMixin, BaseEstimator):
    def __init__(
        self,
        kernel=None,
        *,
        alpha=1e-10,
        optimizer="fmin_l_bfgs_b",
        n_restarts_optimizer=0,
        normalize_y=False,
        copy_X_train=True,
        n_targets=None,
        random_state=None,
    ):
        ...

    def fit(self, X, y):
        ...

    def predict(self, X, return_std=False, return_cov=False):
        ...

    def sample_y(self, X, n_samples=1, random_state=0):
        ...

    def log_marginal_likelihood(self, theta=None, eval_gradient=False, clone_kernel=True):
        ...

Import

from sklearn.gaussian_process import GaussianProcessRegressor

I/O Contract

Inputs

Name	Type	Required	Description
X	array-like of shape (n_samples, n_features)	Yes	Training input samples
y	array-like of shape (n_samples,) or (n_samples, n_targets)	Yes	Target values
kernel	Kernel instance	No	Covariance function (default: ConstantKernel * RBF)
alpha	float or ndarray	No	Noise level added to diagonal of kernel matrix
normalize_y	bool	No	Whether to normalize target values
return_std	bool	No	Whether to return standard deviations with predictions
return_cov	bool	No	Whether to return full covariance matrix with predictions

Outputs

Name	Type	Description
y_mean	ndarray of shape (n_samples,)	Mean prediction
y_std	ndarray of shape (n_samples,)	Standard deviation of prediction (if return_std=True)
y_cov	ndarray of shape (n_samples, n_samples)	Covariance matrix (if return_cov=True)
kernel_	Kernel	Optimized kernel with fitted hyperparameters

Usage Examples

Basic Usage

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

X_train = np.array([[1], [3], [5], [6], [7]])
y_train = np.sin(X_train).ravel()

kernel = C(1.0) * RBF(1.0)
gpr = GaussianProcessRegressor(kernel=kernel, random_state=42)
gpr.fit(X_train, y_train)

X_test = np.linspace(0, 8, 50).reshape(-1, 1)
y_pred, y_std = gpr.predict(X_test, return_std=True)
print(f"Predictions shape: {y_pred.shape}, Std shape: {y_std.shape}")

Related Pages

• Principle:Scikit_learn_Scikit_learn_Gaussian_Process