package sklearn

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Module Kernels.RBFSource

Sourcetype tag = [
  1. | `RBF
]
Sourcetype t = [ `NormalizedKernelMixin | `Object | `RBF | `StationaryKernelMixin ] Obj.t
Sourceval of_pyobject : Py.Object.t -> t
Sourceval to_pyobject : [> tag ] Obj.t -> Py.Object.t
Sourceval as_normalized_kernel : t -> [ `NormalizedKernelMixin ] Obj.t
Sourceval as_stationary_kernel : t -> [ `StationaryKernelMixin ] Obj.t
Sourceval create : ?length_scale:[> `ArrayLike ] Np.Obj.t -> ?length_scale_bounds:[ `Tuple of float * float | `Fixed ] -> unit -> t

Radial-basis function kernel (aka squared-exponential kernel).

The RBF kernel is a stationary kernel. It is also known as the 'squared exponential' kernel. It is parameterized by a length scale parameter :math:`l>0`, which can either be a scalar (isotropic variant of the kernel) or a vector with the same number of dimensions as the inputs X (anisotropic variant of the kernel). The kernel is given by:

.. math:: k(x_i, x_j) = \exp\left(- \fracd(x_i, x_j)^2

l^2

\right)

where :math:`l` is the length scale of the kernel and :math:`d(\cdot,\cdot)` is the Euclidean distance. For advice on how to set the length scale parameter, see e.g. 1_.

This kernel is infinitely differentiable, which implies that GPs with this kernel as covariance function have mean square derivatives of all orders, and are thus very smooth. See 2_, Chapter 4, Section 4.2, for further details of the RBF kernel.

Read more in the :ref:`User Guide <gp_kernels>`.

.. versionadded:: 0.18

Parameters ---------- length_scale : float or ndarray of shape (n_features,), default=1.0 The length scale of the kernel. If a float, an isotropic kernel is used. If an array, an anisotropic kernel is used where each dimension of l defines the length-scale of the respective feature dimension.

length_scale_bounds : pair of floats >= 0 or 'fixed', default=(1e-5, 1e5) The lower and upper bound on 'length_scale'. If set to 'fixed', 'length_scale' cannot be changed during hyperparameter tuning.

References ---------- .. 1 `David Duvenaud (2014). 'The Kernel Cookbook: Advice on Covariance functions'. <https://www.cs.toronto.edu/~duvenaud/cookbook/>`_

.. 2 `Carl Edward Rasmussen, Christopher K. I. Williams (2006). 'Gaussian Processes for Machine Learning'. The MIT Press. <http://www.gaussianprocess.org/gpml/>`_

Examples -------- >>> from sklearn.datasets import load_iris >>> from sklearn.gaussian_process import GaussianProcessClassifier >>> from sklearn.gaussian_process.kernels import RBF >>> X, y = load_iris(return_X_y=True) >>> kernel = 1.0 * RBF(1.0) >>> gpc = GaussianProcessClassifier(kernel=kernel, ... random_state=0).fit(X, y) >>> gpc.score(X, y) 0.9866... >>> gpc.predict_proba(X:2,:) array([0.8354..., 0.03228..., 0.1322...], [0.7906..., 0.0652..., 0.1441...])

Sourceval clone_with_theta : theta:[> `ArrayLike ] Np.Obj.t -> [> tag ] Obj.t -> Py.Object.t

Returns a clone of self with given hyperparameters theta.

Parameters ---------- theta : ndarray of shape (n_dims,) The hyperparameters

Sourceval diag : x:[> `ArrayLike ] Np.Obj.t -> [> tag ] Obj.t -> [> `ArrayLike ] Np.Obj.t

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 : ndarray of shape (n_samples_X, n_features) Left argument of the returned kernel k(X, Y)

Returns ------- K_diag : ndarray of shape (n_samples_X,) Diagonal of kernel k(X, X)

Sourceval get_params : ?deep:bool -> [> tag ] Obj.t -> Dict.t

Get parameters of this kernel.

Parameters ---------- deep : bool, default=True If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns ------- params : dict Parameter names mapped to their values.

Sourceval is_stationary : [> tag ] Obj.t -> Py.Object.t

Returns whether the kernel is stationary.

Sourceval set_params : ?params:(string * Py.Object.t) list -> [> tag ] Obj.t -> t

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

Sourceval to_string : t -> string

Print the object to a human-readable representation.

Sourceval show : t -> string

Print the object to a human-readable representation.

Sourceval pp : Format.formatter -> t -> unit

Pretty-print the object to a formatter.