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

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.


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


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))[source]

Returns the log-transformed bounds on the theta.


bounds : array, shape (n_dims, 2)

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


Returns a clone of self with given hyperparameters theta.


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.


X : array, shape (n_samples_X, n_features)

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


K_diag : array, shape (n_samples_X,)

Diagonal of kernel k(X, X)


Get parameters of this kernel.


deep: boolean, optional :

If True, will return the parameters for this estimator and contained subobjects that are estimators.


params : mapping of string to any

Parameter names mapped to their values.


Returns a list of all hyperparameter specifications.


Returns whether the kernel is stationary.


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


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 :

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.


theta : array, shape (n_dims,)

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