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))

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

Parameters:

length_scale : float > 0, default: 1.0

The length scale of the kernel.

periodicity : float > 0, default: 1.0

The periodicity of the kernel.

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

The lower and upper bound on length_scale

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

The lower and upper bound on periodicity

Methods

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__(length_scale=1.0, periodicity=1.0, length_scale_bounds=(1e-05, 100000.0), periodicity_bounds=(1e-05, 100000.0))

bounds

Returns the log-transformed bounds on the theta.

Returns:

bounds : array, shape (n_dims, 2)

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

clone_with_theta(theta)

Returns a clone of self with given hyperparameters theta.

diag(X)

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:

X : array, shape (n_samples_X, n_features)

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

Returns:

K_diag : array, shape (n_samples_X,)

Diagonal of kernel k(X, X)

get_params(deep=True)

Get parameters of this kernel.

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.

hyperparameters

Returns a list of all hyperparameter specifications.

is_stationary()

Returns whether the kernel is stationary.

n_dims

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

set_params(**params)

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 :

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:

theta : array, shape (n_dims,)

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

Examples using sklearn.gaussian_process.kernels.ExpSineSquared

Illustration of prior and posterior Gaussian process for different kernels

Gaussian process regression (GPR) on Mauna Loa CO2 data.

Comparison of kernel ridge and Gaussian process regression