class sklearn.gaussian_process.kernels.PairwiseKernel(gamma=1.0, gamma_bounds=(1e-05, 100000.0), metric=’linear’, pairwise_kernels_kwargs=None)[source]

Wrapper for kernels in sklearn.metrics.pairwise.

A thin wrapper around the functionality of the kernels in sklearn.metrics.pairwise.

Note: Evaluation of eval_gradient is not analytic but numeric and all
kernels support only isotropic distances. The parameter gamma is considered to be a hyperparameter and may be optimized. The other kernel parameters are set directly at initialization and are kept fixed.

New in version 0.18.


gamma: float >= 0, default: 1.0 :

Parameter gamma of the pairwise kernel specified by metric

gamma_bounds : pair of floats >= 0, default: (1e-5, 1e5)

The lower and upper bound on gamma

metric : string, or callable, default: “linear”

The metric to use when calculating kernel between instances in a feature array. If metric is a string, it must be one of the metrics in pairwise.PAIRWISE_KERNEL_FUNCTIONS. If metric is “precomputed”, X is assumed to be a kernel matrix. Alternatively, if metric is a callable function, it is called on each pair of instances (rows) and the resulting value recorded. The callable should take two arrays from X as input and return a value indicating the distance between them.

pairwise_kernels_kwargs : dict, default: None

All entries of this dict (if any) are passed as keyword arguments to the pairwise kernel function.


clone_with_theta(theta) Returns a clone of self with given hyperparameters theta.
diag(X) Returns the diagonal of the kernel k(X, X).
get_params([deep]) Get parameters of this kernel.
is_stationary() Returns whether the kernel is stationary.
set_params(**params) Set the parameters of this kernel.
__init__(gamma=1.0, gamma_bounds=(1e-05, 100000.0), metric=’linear’, pairwise_kernels_kwargs=None)[source]
__call__(X, Y=None, eval_gradient=False)[source]

Return the kernel k(X, Y) and optionally its gradient.


X : array, shape (n_samples_X, n_features)

Left argument of the returned kernel k(X, Y)

Y : array, shape (n_samples_Y, n_features), (optional, default=None)

Right argument of the returned kernel k(X, Y). If None, k(X, X) if evaluated instead.

eval_gradient : bool (optional, default=False)

Determines whether the gradient with respect to the kernel hyperparameter is determined. Only supported when Y is None.


K : array, shape (n_samples_X, n_samples_Y)

Kernel k(X, Y)

K_gradient : array (opt.), shape (n_samples_X, n_samples_X, n_dims)

The gradient of the kernel k(X, X) with respect to the hyperparameter of the kernel. Only returned when eval_gradient is True.


Returns the log-transformed bounds on the theta.


bounds : array, shape (n_dims, 2)

The log-transformed bounds on the kernel’s hyperparameters theta


Returns a clone of self with given hyperparameters theta.


Returns the diagonal of the kernel k(X, X).

The result of this method is identical to np.diag(self(X)); however, it can be evaluated more efficiently since only the diagonal is evaluated.


X : array, shape (n_samples_X, n_features)

Left argument of the returned kernel k(X, Y)


K_diag : array, shape (n_samples_X,)

Diagonal of kernel k(X, X)


Get parameters of this kernel.


deep : boolean, optional

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


params : mapping of string to any

Parameter names mapped to their values.


Returns a list of all hyperparameter specifications.


Returns whether the kernel is stationary.


Returns the number of non-fixed hyperparameters of the kernel.


Set the parameters of this kernel.

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

Returns:self :

Returns the (flattened, log-transformed) non-fixed hyperparameters.

Note that theta are typically the log-transformed values of the kernel’s hyperparameters as this representation of the search space is more amenable for hyperparameter search, as hyperparameters like length-scales naturally live on a log-scale.


theta : array, shape (n_dims,)

The non-fixed, log-transformed hyperparameters of the kernel