`sklearn.gaussian_process.kernels`.PairwiseKernel#

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.

Parameters:

gammafloat, default=1.0: Parameter gamma of the pairwise kernel specified by metric. It should be positive.
gamma_boundspair of floats >= 0 or “fixed”, default=(1e-5, 1e5): The lower and upper bound on ‘gamma’. If set to “fixed”, ‘gamma’ cannot be changed during hyperparameter tuning.
metric{“linear”, “additive_chi2”, “chi2”, “poly”, “polynomial”, “rbf”, “laplacian”, “sigmoid”, “cosine”} 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_kwargsdict, default=None: All entries of this dict (if any) are passed as keyword arguments to the pairwise kernel function.

Attributes:

bounds: Returns the log-transformed bounds on the theta.
hyperparameter_gamma
hyperparameters: Returns a list of all hyperparameter specifications.
n_dims: Returns the number of non-fixed hyperparameters of the kernel.
requires_vector_input: Returns whether the kernel is defined on fixed-length feature vectors or generic objects.
theta: Returns the (flattened, log-transformed) non-fixed hyperparameters.

Examples

>>> from sklearn.datasets import load_iris
>>> from sklearn.gaussian_process import GaussianProcessClassifier
>>> from sklearn.gaussian_process.kernels import PairwiseKernel
>>> X, y = load_iris(return_X_y=True)
>>> kernel = PairwiseKernel(metric='rbf')
>>> gpc = GaussianProcessClassifier(kernel=kernel,
...         random_state=0).fit(X, y)
>>> gpc.score(X, y)
0.9733...
>>> gpc.predict_proba(X[:2,:])
array([[0.8880..., 0.05663..., 0.05532...],
       [0.8676..., 0.07073..., 0.06165...]])

Methods

`__call__`(X[, Y, eval_gradient])	Return the kernel k(X, Y) and optionally its gradient.
`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.

__call__(X, Y=None, eval_gradient=False)[source]#

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

Parameters:

Xndarray of shape (n_samples_X, n_features): Left argument of the returned kernel k(X, Y)
Yndarray of shape (n_samples_Y, n_features), default=None: Right argument of the returned kernel k(X, Y). If None, k(X, X) if evaluated instead.
eval_gradientbool, default=False: Determines whether the gradient with respect to the log of the kernel hyperparameter is computed. Only supported when Y is None.

Returns:

Kndarray of shape (n_samples_X, n_samples_Y): Kernel k(X, Y)
K_gradientndarray of shape (n_samples_X, n_samples_X, n_dims), optional: The gradient of the kernel k(X, X) with respect to the log of the hyperparameter of the kernel. Only returned when eval_gradient is True.

property bounds#

Returns the log-transformed bounds on the theta.

Returns:

boundsndarray of shape (n_dims, 2): The log-transformed bounds on the kernel’s hyperparameters theta

clone_with_theta(theta)[source]#

Returns a clone of self with given hyperparameters theta.

Parameters:

thetandarray of shape (n_dims,): The hyperparameters

diag(X)[source]#

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.

Parameters:

Xndarray of shape (n_samples_X, n_features): Left argument of the returned kernel k(X, Y)

Returns:

K_diagndarray of shape (n_samples_X,): Diagonal of kernel k(X, X)

get_params(deep=True)[source]#

Get parameters of this kernel.

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.

property hyperparameters#: Returns a list of all hyperparameter specifications.

is_stationary()[source]#: Returns whether the kernel is stationary.

property n_dims#: Returns the number of non-fixed hyperparameters of the kernel.

property requires_vector_input#: Returns whether the kernel is defined on fixed-length feature vectors or generic objects. Defaults to True for backward compatibility.

set_params(**params)[source]#

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

property theta#

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.

Returns:

thetandarray of shape (n_dims,): The non-fixed, log-transformed hyperparameters of the kernel

sklearn.gaussian_process.kernels.PairwiseKernel#

`sklearn.gaussian_process.kernels`.PairwiseKernel#