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 \(\sigma\) which controls the inhomogenity of the kernel. 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.
See [1], Chapter 4, Section 4.2, for further details regarding the DotProduct kernel.
Read more in the User Guide.
New in version 0.18.
- Parameters
- sigma_0float >= 0, default=1.0
Parameter controlling the inhomogenity of the kernel. If sigma_0=0, the kernel is homogenous.
- sigma_0_boundspair of floats >= 0 or “fixed”, default=(1e-5, 1e5)
The lower and upper bound on ‘sigma_0’. If set to “fixed”, ‘sigma_0’ cannot be changed during hyperparameter tuning.
- Attributes
boundsReturns the log-transformed bounds on the theta.
- hyperparameter_sigma_0
hyperparametersReturns a list of all hyperparameter specifications.
n_dimsReturns the number of non-fixed hyperparameters of the kernel.
requires_vector_inputReturns whether the kernel is defined on fixed-length feature vectors or generic objects.
thetaReturns the (flattened, log-transformed) non-fixed hyperparameters.
References
Examples
>>> from sklearn.datasets import make_friedman2 >>> from sklearn.gaussian_process import GaussianProcessRegressor >>> from sklearn.gaussian_process.kernels import DotProduct, WhiteKernel >>> X, y = make_friedman2(n_samples=500, noise=0, random_state=0) >>> kernel = DotProduct() + WhiteKernel() >>> gpr = GaussianProcessRegressor(kernel=kernel, ... random_state=0).fit(X, y) >>> gpr.score(X, y) 0.3680... >>> gpr.predict(X[:2,:], return_std=True) (array([653.0..., 592.1...]), array([316.6..., 316.6...]))
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.
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__init__(sigma_0=1.0, sigma_0_bounds=(1e-05, 100000.0))[source]¶ Initialize self. See help(type(self)) for accurate signature.
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__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 kernel hyperparameter is determined. 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 hyperparameter of the kernel. Only returned when
eval_gradientis True.
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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
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clone_with_theta(theta)[source]¶ Returns a clone of self with given hyperparameters theta.
- Parameters
- thetandarray of shape (n_dims,)
The hyperparameters
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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
- 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).
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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.
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property
hyperparameters¶ Returns a list of all hyperparameter specifications.
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property
n_dims¶ Returns the number of non-fixed hyperparameters of the kernel.
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property
requires_vector_input¶ Returns whether the kernel is defined on fixed-length feature vectors or generic objects. Defaults to True for backward compatibility.
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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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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
