`sklearn.gaussian_process.kernels`.RBF¶

class sklearn.gaussian_process.kernels.RBF(length_scale=1.0, length_scale_bounds=(1e-05, 100000.0))[source]¶

Radial-basis function kernel (aka squared-exponential kernel).

The RBF kernel is a stationary kernel. It is also known as the “squared exponential” kernel. It is parameterized by a length-scale parameter length_scale>0, which can either be a scalar (isotropic variant of the kernel) or a vector with the same number of dimensions as the inputs X (anisotropic variant of the kernel). The kernel is given by:

k(x_i, x_j) = exp(-1 / 2 d(x_i / length_scale, x_j / length_scale)^2)

This kernel is infinitely differentiable, which implies that GPs with this kernel as covariance function have mean square derivatives of all orders, and are thus very smooth.

New in version 0.18.

Parameters

length_scalefloat or array with shape (n_features,), default: 1.0: The length scale of the kernel. If a float, an isotropic kernel is used. If an array, an anisotropic kernel is used where each dimension of l defines the length-scale of the respective feature dimension.
length_scale_boundspair of floats >= 0, default: (1e-5, 1e5): The lower and upper bound on length_scale

Attributes

anisotropic
bounds: Returns the log-transformed bounds on the theta.
hyperparameter_length_scale
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.

Methods

`__call__`(self, X[, Y, eval_gradient])	Return the kernel k(X, Y) and optionally its gradient.
`clone_with_theta`(self, theta)	Returns a clone of self with given hyperparameters theta.
`diag`(self, X)	Returns the diagonal of the kernel k(X, X).
`get_params`(self[, deep])	Get parameters of this kernel.
`is_stationary`(self)	Returns whether the kernel is stationary.
`set_params`(self, \\params)	Set the parameters of this kernel.

__init__(self, length_scale=1.0, length_scale_bounds=(1e-05, 100000.0))[source]¶: Initialize self. See help(type(self)) for accurate signature.

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

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

Parameters

Xarray, shape (n_samples_X, n_features): Left argument of the returned kernel k(X, Y)
Yarray, 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_gradientbool (optional, default=False): Determines whether the gradient with respect to the kernel hyperparameter is determined. Only supported when Y is None.

Returns

Karray, shape (n_samples_X, n_samples_Y): Kernel k(X, Y)
K_gradientarray (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.

property bounds¶

Returns the log-transformed bounds on the theta.

Returns

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

clone_with_theta(self, theta)[source]¶

Returns a clone of self with given hyperparameters theta.

Parameters

thetaarray, shape (n_dims,): The hyperparameters

diag(self, 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

Xsequence of length n_samples: Left argument of the returned kernel k(X, Y)

Returns

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

get_params(self, deep=True)[source]¶

Get parameters of this kernel.

Parameters

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

Returns

paramsmapping of string to any: Parameter names mapped to their values.

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

is_stationary(self)[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(self, **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