sklearn.gaussian_process.kernels.DotProduct

class sklearn.gaussian_process.kernels.DotProduct(sigma_0=1.0, sigma_0_bounds=(1e-05, 100000.0))

Dot-Product kernel.

The DotProduct kernel is non-stationary and can be obtained from linear regression by putting N(0, 1) priors on the coefficients of x_d (d = 1, . . . , D) and a prior of N(0, sigma_0^2) on the bias. The DotProduct kernel is invariant to a rotation of the coordinates about the origin, but not translations. It is parameterized by a parameter sigma_0^2. For sigma_0^2 =0, the kernel is called the homogeneous linear kernel, otherwise it is inhomogeneous. The kernel is given by

k(x_i, x_j) = sigma_0 ^ 2 + x_i cdot x_j

The DotProduct kernel is commonly combined with exponentiation.

New in version 0.18.

Parameters:

sigma_0 : float >= 0, default: 1.0

Parameter controlling the inhomogenity of the kernel. If sigma_0=0, the kernel is homogenous.

sigma_0_bounds : pair of floats >= 0, default: (1e-5, 1e5)

The lower and upper bound on l

Attributes:

bounds

Returns the log-transformed bounds on the theta.

hyperparameter_sigma_0

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__(X[, Y, eval_gradient])	Return the kernel k(X, Y) and optionally its gradient.
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__(sigma_0=1.0, sigma_0_bounds=(1e-05, 100000.0))

__call__(X, Y=None, eval_gradient=False)

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

Parameters:

X : array, shape (n_samples_X, n_features)

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

Y : array, 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_gradient : bool (optional, default=False)

Determines whether the gradient with respect to the kernel hyperparameter is determined. Only supported when Y is None.

Returns:

K : array, shape (n_samples_X, n_samples_Y)

Kernel k(X, Y)

K_gradient : array (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.

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.

Parameters:

theta : array, shape (n_dims,)

The hyperparameters

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.DotProduct

Illustration of Gaussian process classification (GPC) on the XOR dataset

Illustration of prior and posterior Gaussian process for different kernels

Iso-probability lines for Gaussian Processes classification (GPC)