RationalQuadratic#
- class sklearn.gaussian_process.kernels.RationalQuadratic(length_scale=1.0, alpha=1.0, length_scale_bounds=(1e-05, 100000.0), alpha_bounds=(1e-05, 100000.0))[source]#
Rational Quadratic kernel.
The RationalQuadratic kernel can be seen as a scale mixture (an infinite sum) of RBF kernels with different characteristic length scales. It is parameterized by a length scale parameter
and a scale mixture parameter . Only the isotropic variant where length_scale is a scalar is supported at the moment. The kernel is given by:where
is the scale mixture parameter, is the length scale of the kernel and is the Euclidean distance. For advice on how to set the parameters, see e.g. [1].Read more in the User Guide.
Added in version 0.18.
- Parameters:
- length_scalefloat > 0, default=1.0
The length scale of the kernel.
- alphafloat > 0, default=1.0
Scale mixture parameter
- length_scale_boundspair 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.
- alpha_boundspair of floats >= 0 or “fixed”, default=(1e-5, 1e5)
The lower and upper bound on ‘alpha’. If set to “fixed”, ‘alpha’ cannot be changed during hyperparameter tuning.
References
Examples
>>> from sklearn.datasets import load_iris >>> from sklearn.gaussian_process import GaussianProcessClassifier >>> from sklearn.gaussian_process.kernels import RationalQuadratic >>> X, y = load_iris(return_X_y=True) >>> kernel = RationalQuadratic(length_scale=1.0, alpha=1.5) >>> gpc = GaussianProcessClassifier(kernel=kernel, ... random_state=0).fit(X, y) >>> gpc.score(X, y) 0.9733... >>> gpc.predict_proba(X[:2,:]) array([[0.8881..., 0.0566..., 0.05518...], [0.8678..., 0.0707... , 0.0614...]])
- __call__(X, Y=None, eval_gradient=False)[source]#
Return the kernel k(X, Y) and optionally its gradient.
- Parameters:
- Xndarray of shape (n_samples_X, n_features)
Left argument of the returned kernel k(X, Y)
- Yndarray of shape (n_samples_Y, n_features), default=None
Right argument of the returned kernel k(X, Y). If None, k(X, X) if 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)
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:
- Xndarray of shape (n_samples_X, n_features)
Left argument of the returned kernel k(X, Y)
- 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#
Returns whether the kernel is defined on fixed-length feature vectors or generic objects. Defaults to True for backward compatibility.
- 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
Gallery examples#
Forecasting of CO2 level on Mona Loa dataset using Gaussian process regression (GPR)
Illustration of prior and posterior Gaussian process for different kernels