`sklearn.kernel_ridge`.KernelRidge¶

class sklearn.kernel_ridge.KernelRidge(alpha=1, *, kernel='linear', gamma=None, degree=3, coef0=1, kernel_params=None)[source]¶

Kernel ridge regression.

Kernel ridge regression (KRR) combines ridge regression (linear least squares with l2-norm regularization) with the kernel trick. It thus learns a linear function in the space induced by the respective kernel and the data. For non-linear kernels, this corresponds to a non-linear function in the original space.

The form of the model learned by KRR is identical to support vector regression (SVR). However, different loss functions are used: KRR uses squared error loss while support vector regression uses epsilon-insensitive loss, both combined with l2 regularization. In contrast to SVR, fitting a KRR model can be done in closed-form and is typically faster for medium-sized datasets. On the other hand, the learned model is non-sparse and thus slower than SVR, which learns a sparse model for epsilon > 0, at prediction-time.

This estimator has built-in support for multi-variate regression (i.e., when y is a 2d-array of shape [n_samples, n_targets]).

See also

sklearn.gaussian_process.GaussianProcessRegressor: Gaussian Process regressor providing automatic kernel hyperparameters tuning and predictions uncertainty.
sklearn.linear_model.Ridge: Linear ridge regression.
sklearn.linear_model.RidgeCV: Ridge regression with built-in cross-validation.
sklearn.svm.SVR: Support Vector Regression accepting a large variety of kernels.

References

Kevin P. Murphy “Machine Learning: A Probabilistic Perspective”, The MIT Press chapter 14.4.3, pp. 492-493

Examples

>>> from sklearn.kernel_ridge import KernelRidge
>>> import numpy as np
>>> n_samples, n_features = 10, 5
>>> rng = np.random.RandomState(0)
>>> y = rng.randn(n_samples)
>>> X = rng.randn(n_samples, n_features)
>>> krr = KernelRidge(alpha=1.0)
>>> krr.fit(X, y)
KernelRidge(alpha=1.0)

Methods

`fit`(X, y[, sample_weight])	Fit Kernel Ridge regression model.
`get_params`([deep])	Get parameters for this estimator.
`predict`(X)	Predict using the kernel ridge model.
`score`(X, y[, sample_weight])	Return the coefficient of determination of the prediction.
`set_params`(**params)	Set the parameters of this estimator.

fit(X, y, sample_weight=None)[source]¶

Fit Kernel Ridge regression model.

Parameters

X{array-like, sparse matrix} of shape (n_samples, n_features): Training data. If kernel == “precomputed” this is instead a precomputed kernel matrix, of shape (n_samples, n_samples).
yarray-like of shape (n_samples,) or (n_samples, n_targets): Target values.
sample_weightfloat or array-like of shape (n_samples,), default=None: Individual weights for each sample, ignored if None is passed.

Returns

selfobject: Returns the instance itself.

get_params(deep=True)[source]¶

Get parameters for this estimator.

Parameters

deepbool, default=True: If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns

paramsdict: Parameter names mapped to their values.

predict(X)[source]¶

Predict using the kernel ridge model.

Parameters

X{array-like, sparse matrix} of shape (n_samples, n_features): Samples. If kernel == “precomputed” this is instead a precomputed kernel matrix, shape = [n_samples, n_samples_fitted], where n_samples_fitted is the number of samples used in the fitting for this estimator.

Returns

Cndarray of shape (n_samples,) or (n_samples, n_targets): Returns predicted values.

score(X, y, sample_weight=None)[source]¶

Return the coefficient of determination of the prediction.

The coefficient of determination \(R^2\) is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares ((y_true - y_pred)** 2).sum() and \(v\) is the total sum of squares ((y_true - y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a \(R^2\) score of 0.0.

Parameters

Xarray-like of shape (n_samples, n_features): Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
yarray-like of shape (n_samples,) or (n_samples, n_outputs): True values for X.
sample_weightarray-like of shape (n_samples,), default=None: Sample weights.

Returns

scorefloat: \(R^2\) of self.predict(X) wrt. y.

Notes

The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).

set_params(**params)[source]¶

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters

**paramsdict: Estimator parameters.

Returns

selfestimator instance: Estimator instance.

Examples using `sklearn.kernel_ridge.KernelRidge`¶

sklearn.kernel_ridge.KernelRidge¶

Examples using sklearn.kernel_ridge.KernelRidge¶

`sklearn.kernel_ridge`.KernelRidge¶

Examples using `sklearn.kernel_ridge.KernelRidge`¶