Isotropic covariance functions

gpyreg.isotropic_covariance_functions

The isotropic kernels use a single length scale for every input dimension, so they have two hyperparameters whatever the dimensionality. Each is implemented as a subclass of AbstractIsotropicKernel, which fixes those two hyperparameters and the bounds recommended for them (hyperparameter_count, hyperparameter_info and get_bounds_info), and of the kernel of the same family in gpyreg.covariance_functions, from which it inherits the rest, such as the degree of the Matern kernel; each defines its own compute. An instance is passed to gpyreg.GP at initialization in the same way as an anisotropic one.

AbstractIsotropicKernel

class gpyreg.isotropic_covariance_functions.AbstractIsotropicKernel

Bases: AbstractKernel

Abstract base class for isotropic kernel functions.

The two default hyperparameters are the log-lengthscale and log-outputscale.

get_bounds_info(X: ndarray, y: ndarray)

Return information on the lower, upper, plausible lower and plausible upper bounds of the hyperparameters of this covariance function.

Parameters:

Xndarray, shape (N, D)

A 2D array where each row is a test point.

yndarray, shape (N, 1)

A 2D array where each row is a test target.

Returns:

cov_bound_info: dict

A dictionary containing the bound info with the following elements:

LBnp.ndarray, shape (cov_N, 1)

The lower bounds of the hyperparameters.

UBnp.ndarray, shape (cov_N, 1)

The upper bounds of the hyperparameters.

PLBnp.ndarray, shape (cov_N, 1)

The plausible lower bounds of the hyperparameters.

PUBnp.ndarray, shape (cov_N, 1)

The plausible upper bounds of the hyperparameters.

x0np.ndarray, shape (cov_N, 1)

The plausible starting point.

where cov_N is the number of hyperparameters.

hyperparameter_count(D: int)

Return the number of hyperparameters this covariance function has.

Parameters:

Dint

The dimensionality of the kernel.

Returns:

countint

The number of hyperparameters.

hyperparameter_info(D: int)

Return information on the names of hyperparameters for setting them in other parts of the program.

Parameters:

Dint

The dimensionality of the kernel.

Returns:

hyper_infoarray_like

A list of tuples of hyperparameter names and their number, in the order they are in the hyperparameter array.

MaternIsotropic

class gpyreg.isotropic_covariance_functions.MaternIsotropic(degree: int)

Bases: AbstractIsotropicKernel, Matern

Isotropic Matern kernel.

Overrides compute. Inherits hyperparameter_count and hyperparameter_info from AbstractIsotropicKernel. Inherits other methods from Matern.

Parameters:

degree{1, 3, 5}

The degree of the isotropic Matern kernel.

Currently the only supported degrees are 1, 3, 5, and if some other degree is provided a ValueError exception is raised.

compute(hyp: ndarray, X: ndarray, X_star: ndarray = None, compute_diag: bool = False, compute_grad: bool = False)

Compute the covariance matrix for given training points and test points.

Parameters:

hypndarray, shape (cov_N,)

A 1D array of hyperparameters, where cov_N is the number of hyperparameters.

Xndarray, shape (N, D)

A 2D array where each row is a training point.

X_starndarray, shape (M, D), optional

A 2D array where each row is a test point. If this is not given, the self-covariance matrix is being computed.

compute_diagbool, defaults to False

Whether to only compute the diagonal of the self-covariance matrix.

compute_gradbool, defaults to False

Whether to compute the gradient with respect to the hyperparameters.

Returns:

Kndarray

The covariance matrix which is by default of shape (N, N). If compute_diag = True the shape is (N, 1).

dKndarray, shape (N, N, cov_N), optional

The gradient of the covariance matrix with respect to the hyperparameters.

Raises:

ValueError

Raised when hyp has not the expected number of hyperparameters.

ValueError

Raised when hyp is not an 1D array but of higher dimension.

ValueError

Raised when compute_diag and compute_grad are both True: the gradient is available for the full covariance matrix only.

SquaredExponentialIsotropic

class gpyreg.isotropic_covariance_functions.SquaredExponentialIsotropic

Bases: AbstractIsotropicKernel, SquaredExponential

Isotropic squared exponential kernel.

Overrides compute. Inherits hyperparameter_count and hyperparameter_info from AbstractIsotropicKernel. Inherits other methods from SquaredExponential.

compute(hyp: ndarray, X: ndarray, X_star: ndarray = None, compute_diag: bool = False, compute_grad: bool = False)

Compute the covariance matrix for given training points and test points.

Parameters:

hypndarray, shape (cov_N,)

A 1D array of hyperparameters, where cov_N is the number of hyperparameters.

Xndarray, shape (N, D)

A 2D array where each row is a training point.

X_starndarray, shape (M, D), optional

A 2D array where each row is a test point. If this is not given, the self-covariance matrix is being computed.

compute_diagbool, defaults to False

Whether to only compute the diagonal of the self-covariance matrix.

compute_gradbool, defaults to False

Whether to compute the gradient with respect to the hyperparameters.

Returns:

Kndarray

The covariance matrix which is by default of shape (N, N). If compute_diag = True the shape is (N, 1).

dKndarray, shape (N, N, cov_N), optional

The gradient of the covariance matrix with respect to the hyperparameters.

Raises:

ValueError

Raised when hyp has not the expected number of hyperparameters.

ValueError

Raised when hyp is not an 1D array but of higher dimension.

ValueError

Raised when compute_diag and compute_grad are both True: the gradient is available for the full covariance matrix only.