sklearn.gaussian_process.kernels.DotProduct¶
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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.
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
Methods
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. -
__call__(X, Y=None, eval_gradient=False)[source]¶ 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.
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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
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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: 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)
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get_params(deep=True)[source]¶ 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.
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hyperparameters¶ Returns a list of all hyperparameter specifications.
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n_dims¶ Returns the number of non-fixed hyperparameters of the kernel.
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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 :
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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
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