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 l2norm regularization) with the kernel trick. It thus learns a linear function in the space induced by the respective kernel and the data. For nonlinear kernels, this corresponds to a nonlinear 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 epsiloninsensitive loss, both combined with l2 regularization. In contrast to SVR, fitting a KRR model can be done in closedform and is typically faster for mediumsized datasets. On the other hand, the learned model is nonsparse and thus slower than SVR, which learns a sparse model for epsilon > 0, at predictiontime.
This estimator has builtin support for multivariate regression (i.e., when y is a 2darray of shape [n_samples, n_targets]).
Read more in the User Guide.
Parameters: alpha : {float, arraylike}, shape = [n_targets]
Small positive values of alpha improve the conditioning of the problem and reduce the variance of the estimates. Alpha corresponds to
(2*C)^1
in other linear models such as LogisticRegression or LinearSVC. If an array is passed, penalties are assumed to be specific to the targets. Hence they must correspond in number.kernel : string or callable, default=”linear”
Kernel mapping used internally. A callable should accept two arguments and the keyword arguments passed to this object as kernel_params, and should return a floating point number.
gamma : float, default=None
Gamma parameter for the RBF, laplacian, polynomial, exponential chi2 and sigmoid kernels. Interpretation of the default value is left to the kernel; see the documentation for sklearn.metrics.pairwise. Ignored by other kernels.
degree : float, default=3
Degree of the polynomial kernel. Ignored by other kernels.
coef0 : float, default=1
Zero coefficient for polynomial and sigmoid kernels. Ignored by other kernels.
kernel_params : mapping of string to any, optional
Additional parameters (keyword arguments) for kernel function passed as callable object.
Attributes: dual_coef_ : array, shape = [n_samples] or [n_samples, n_targets]
Representation of weight vector(s) in kernel space
X_fit_ : {arraylike, sparse matrix}, shape = [n_samples, n_features]
Training data, which is also required for prediction
See also
Ridge
 Linear ridge regression.
SVR
 Support Vector Regression implemented using libsvm.
References
 Kevin P. Murphy “Machine Learning: A Probabilistic Perspective”, The MIT Press chapter 14.4.3, pp. 492493
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) >>> clf = KernelRidge(alpha=1.0) >>> clf.fit(X, y) KernelRidge(alpha=1.0, coef0=1, degree=3, gamma=None, kernel='linear', kernel_params=None)
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])Returns the coefficient of determination R^2 of the prediction. set_params
(\*\*params)Set the parameters of this estimator. 
fit
(X, y=None, sample_weight=None)[source]¶ Fit Kernel Ridge regression model
Parameters: X : {arraylike, sparse matrix}, shape = [n_samples, n_features]
Training data
y : arraylike, shape = [n_samples] or [n_samples, n_targets]
Target values
sample_weight : float or numpy array of shape [n_samples]
Individual weights for each sample, ignored if None is passed.
Returns: self : returns an instance of self.

get_params
(deep=True)[source]¶ Get parameters for this estimator.
Parameters: deep : boolean, optional
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns: params : mapping of string to any
Parameter names mapped to their values.

predict
(X)[source]¶ Predict using the kernel ridge model
Parameters: X : {arraylike, sparse matrix}, shape = [n_samples, n_features]
Samples.
Returns: C : array, shape = [n_samples] or [n_samples, n_targets]
Returns predicted values.

score
(X, y, sample_weight=None)[source]¶ Returns the coefficient of determination R^2 of the prediction.
The coefficient R^2 is defined as (1  u/v), where u is the regression sum of squares ((y_true  y_pred) ** 2).sum() and v is the residual sum of squares ((y_true  y_true.mean()) ** 2).sum(). 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: X : arraylike, shape = (n_samples, n_features)
Test samples.
y : arraylike, shape = (n_samples) or (n_samples, n_outputs)
True values for X.
sample_weight : arraylike, shape = [n_samples], optional
Sample weights.
Returns: score : float
R^2 of self.predict(X) wrt. y.

set_params
(**params)[source]¶ Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form
<component>__<parameter>
so that it’s possible to update each component of a nested object.Returns: self :