sklearn.gaussian_process.kernels
.ConstantKernel¶
- class sklearn.gaussian_process.kernels.ConstantKernel(constant_value=1.0, constant_value_bounds=(1e-05, 100000.0))[source]¶
Constant kernel.
Can be used as part of a product-kernel where it scales the magnitude of the other factor (kernel) or as part of a sum-kernel, where it modifies the mean of the Gaussian process.
\[k(x_1, x_2) = constant\_value \;\forall\; x_1, x_2\]Adding a constant kernel is equivalent to adding a constant:
kernel = RBF() + ConstantKernel(constant_value=2)
is the same as:
kernel = RBF() + 2
Read more in the User Guide.
New in version 0.18.
- Parameters
- constant_valuefloat, default=1.0
The constant value which defines the covariance: k(x_1, x_2) = constant_value
- constant_value_boundspair of floats >= 0 or “fixed”, default=(1e-5, 1e5)
The lower and upper bound on
constant_value
. If set to “fixed”,constant_value
cannot be changed during hyperparameter tuning.
- Attributes
bounds
Returns the log-transformed bounds on the theta.
- hyperparameter_constant_value
hyperparameters
Returns a list of all hyperparameter specifications.
n_dims
Returns the number of non-fixed hyperparameters of the kernel.
requires_vector_input
Whether the kernel works only on fixed-length feature vectors.
theta
Returns the (flattened, log-transformed) non-fixed hyperparameters.
Examples
>>> from sklearn.datasets import make_friedman2 >>> from sklearn.gaussian_process import GaussianProcessRegressor >>> from sklearn.gaussian_process.kernels import RBF, ConstantKernel >>> X, y = make_friedman2(n_samples=500, noise=0, random_state=0) >>> kernel = RBF() + ConstantKernel(constant_value=2) >>> gpr = GaussianProcessRegressor(kernel=kernel, alpha=5, ... random_state=0).fit(X, y) >>> gpr.score(X, y) 0.3696... >>> gpr.predict(X[:1,:], return_std=True) (array([606.1...]), array([0.24...]))
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.
Returns whether the kernel is stationary.
set_params
(**params)Set the parameters of this kernel.
- __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. Only supported when Y is None.
- 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 specifications.
- property n_dims¶
Returns the number of non-fixed hyperparameters of the kernel.
- property requires_vector_input¶
Whether the kernel works only on fixed-length feature vectors.
- 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