# Sum#

class sklearn.gaussian_process.kernels.Sum(k1, k2)[source]#

The Sum kernel takes two kernels $$k_1$$ and $$k_2$$ and combines them via

$k_{sum}(X, Y) = k_1(X, Y) + k_2(X, Y)$

Note that the __add__ magic method is overridden, so Sum(RBF(), RBF()) is equivalent to using the + operator with RBF() + RBF().

Read more in the User Guide.

Added in version 0.18.

Parameters:
k1Kernel

The first base-kernel of the sum-kernel

k2Kernel

The second base-kernel of the sum-kernel

Examples

>>> from sklearn.datasets import make_friedman2
>>> from sklearn.gaussian_process import GaussianProcessRegressor
>>> from sklearn.gaussian_process.kernels import RBF, Sum, ConstantKernel
>>> X, y = make_friedman2(n_samples=500, noise=0, random_state=0)
>>> kernel = Sum(ConstantKernel(2), RBF())
>>> gpr = GaussianProcessRegressor(kernel=kernel,
...         random_state=0).fit(X, y)
>>> gpr.score(X, y)
1.0
>>> kernel
1.41**2 + RBF(length_scale=1)

__call__(X, Y=None, eval_gradient=False)[source]#

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

Parameters:
Xarray-like of shape (n_samples_X, n_features) or list of object

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

Yarray-like of shape (n_samples_X, n_features) or list of object, default=None

Right argument of the returned kernel k(X, Y). If None, k(X, X) is evaluated instead.

eval_gradientbool, default=False

Determines whether the gradient with respect to the log of the kernel hyperparameter is computed.

Returns:
Kndarray of shape (n_samples_X, n_samples_Y)

Kernel k(X, Y)

K_gradientndarray of shape (n_samples_X, n_samples_X, n_dims), optional

The gradient of the kernel k(X, X) with respect to the log of the hyperparameter of the kernel. Only returned when eval_gradient is True.

property bounds#

Returns the log-transformed bounds on the theta.

Returns:
boundsndarray of 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.

Parameters:
thetandarray of shape (n_dims,)

The hyperparameters

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:
Xarray-like of shape (n_samples_X, n_features) or list of object

Argument to the kernel.

Returns:
K_diagndarray of shape (n_samples_X,)

Diagonal of kernel k(X, X)

get_params(deep=True)[source]#

Get parameters of this kernel.

Parameters:
deepbool, default=True

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

Returns:
paramsdict

Parameter names mapped to their values.

property hyperparameters#

Returns a list of all hyperparameter.

is_stationary()[source]#

Returns whether the kernel is stationary.

property n_dims#

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

property requires_vector_input#

Returns whether the kernel is stationary.

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
property 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:
thetandarray of shape (n_dims,)

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