sklearn.gaussian_process.kernels.ExpSineSquared¶

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

Exp-Sine-Squared kernel.

The ExpSineSquared kernel allows modeling periodic functions. It is parameterized by a length-scale parameter length_scale>0 and a periodicity parameter periodicity>0. Only the isotropic variant where l is a scalar is supported at the moment. The kernel given by:

k(x_i, x_j) = exp(-2 (sin(pi / periodicity * d(x_i, x_j)) / length_scale) ^ 2)

New in version 0.18.

Parameters
length_scalefloat > 0, default: 1.0

The length scale of the kernel.

periodicityfloat > 0, default: 1.0

The periodicity of the kernel.

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

The lower and upper bound on length_scale

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

The lower and upper bound on periodicity

Attributes
bounds

Returns the log-transformed bounds on the theta.

hyperparameter_length_scale
hyperparameter_periodicity
hyperparameters

Returns a list of all hyperparameter specifications.

n_dims

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

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, periodicity=1.0, length_scale_bounds=(1e-05, 100000.0), periodicity_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.

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
Xarray, shape (n_samples_X, n_features)

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.

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
thetaarray, shape (n_dims,)

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