Implementation:Scikit learn Scikit learn GaussianProcessClassifier

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

Overview

Concrete implementation of Gaussian Process Classification (GPC) provided by scikit-learn.

Description

The GaussianProcessClassifier implements Gaussian process classification based on Laplace approximation. For binary classification, it uses _BinaryGaussianProcessClassifierLaplace internally. For multiclass problems, it wraps the binary classifier using either one-vs-rest or one-vs-one strategies. The kernel hyperparameters are optimized during fitting via L-BFGS-B. The module provides both class predictions and calibrated probability estimates.

Usage

Use Gaussian Process Classification when you need probabilistic predictions with uncertainty estimates, particularly for small to medium-sized datasets. GPC provides well-calibrated class probabilities and works well when the kernel captures the underlying data structure.

Code Reference

Source Location

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

Signature

class _BinaryGaussianProcessClassifierLaplace(BaseEstimator):
    def __init__(self, kernel=None, *, optimizer="fmin_l_bfgs_b",
                 n_restarts_optimizer=0, max_iter_predict=100,
                 warm_start=False, copy_X_train=True, random_state=None):
        ...

class GaussianProcessClassifier(ClassifierMixin, BaseEstimator):
    def __init__(self, kernel=None, *, optimizer="fmin_l_bfgs_b",
                 n_restarts_optimizer=0, max_iter_predict=100,
                 warm_start=False, copy_X_train=True, random_state=None,
                 multi_class="one_vs_rest", n_jobs=None):
        ...

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

    def predict(self, X):
        ...

    def predict_proba(self, X):
        ...

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

Import

from sklearn.gaussian_process import GaussianProcessClassifier

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,)	Yes	Target class labels
kernel	Kernel instance	No	Covariance function (default: 1.0 * RBF(1.0))
optimizer	str or callable	No	Optimizer for kernel hyperparameters
n_restarts_optimizer	int	No	Number of optimizer restarts
multi_class	str	No	Multiclass strategy: "one_vs_rest" or "one_vs_one"

Outputs

Name	Type	Description
predictions	ndarray of shape (n_samples,)	Predicted class labels
probabilities	ndarray of shape (n_samples, n_classes)	Class probability estimates
log_marginal_likelihood_value_	float	Log marginal likelihood of the fitted model
kernel_	Kernel	Optimized kernel with fitted hyperparameters

Usage Examples

Basic Usage

from sklearn.gaussian_process import GaussianProcessClassifier
from sklearn.gaussian_process.kernels import RBF
from sklearn.datasets import make_classification

X, y = make_classification(n_samples=100, n_features=2, random_state=42)
kernel = 1.0 * RBF(1.0)
gpc = GaussianProcessClassifier(kernel=kernel, random_state=42)
gpc.fit(X, y)
proba = gpc.predict_proba(X[:5])
print(proba)

Related Pages

• Principle:Scikit_learn_Scikit_learn_Gaussian_Process