gaussian_process.kernels.RationalQuadratic()

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

Rational Quadratic kernel.

The RationalQuadratic kernel can be seen as a scale mixture (an infinite sum) of RBF kernels with different characteristic length-scales. It is parameterized by a length-scale parameter length_scale>0 and a scale mixture parameter alpha>0. Only the isotropic variant where length_scale is a scalar is supported at the moment. The kernel given by:

k(x_i, x_j) = (1 + d(x_i, x_j)^2 / (2*alpha * length_scale^2))^-alpha

New in version 0.18.

Parameters:

Parameters:	length_scale : float > 0, default: 1.0 The length scale of the kernel. alpha : float > 0, default: 1.0 Scale mixture parameter length_scale_bounds : pair of floats >= 0, default: (1e-5, 1e5) The lower and upper bound on length_scale alpha_bounds : pair of floats >= 0, default: (1e-5, 1e5) The lower and upper bound on alpha

length_scale : float > 0, default: 1.0

The length scale of the kernel.

alpha : float > 0, default: 1.0

Scale mixture parameter

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

The lower and upper bound on length_scale

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

The lower and upper bound on alpha

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, alpha=1.0, length_scale_bounds=(1e-05, 100000.0), alpha_bounds=(1e-05, 100000.0)) [source]

bounds

Returns the log-transformed bounds on the theta.

Returns:

Returns:	bounds : array, shape (n_dims, 2) The log-transformed bounds on the kernel?s hyperparameters theta

bounds : array, 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.

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:

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)

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) [source]

Get parameters of this kernel.

Parameters:

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.

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

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

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 :

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: