sklearn.gaussian_process.kernels.WhiteKernel  
class sklearn.gaussian_process.kernels.WhiteKernel(noise_level=1.0, noise_level_bounds=1e-05, 100000.0) [source]
 
White kernel. The main use-case of this kernel is as part of a sum-kernel where it explains the noise of the signal as independently and identically normally-distributed. The parameter noise_level equals the variance of this noise.  \[k(x_1, x_2) = noise\_level \text{ if } x_i == x_j \text{ else } 0\] Read more in the User Guide.  New in version 0.18.   Parameters 
 
noise_levelfloat, default=1.0 

Parameter controlling the noise level (variance)  
noise_level_boundspair of floats >= 0 or “fixed”, default=(1e-5, 1e5) 

The lower and upper bound on ‘noise_level’. If set to “fixed”, ‘noise_level’ cannot be changed during hyperparameter tuning.    Attributes 
 
bounds


Returns the log-transformed bounds on the theta.  hyperparameter_noise_level

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 DotProduct, WhiteKernel
>>> X, y = make_friedman2(n_samples=500, noise=0, random_state=0)
>>> kernel = DotProduct() + WhiteKernel(noise_level=0.5)
>>> 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.  
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 
 
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. 
  
is_stationary() [source]
 
Returns whether the kernel is stationary. 
  
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     
 
 Examples using sklearn.gaussian_process.kernels.WhiteKernel
 
  Comparison of kernel ridge and Gaussian process regression  

  Gaussian process regression (GPR) with noise-level estimation  

  Gaussian process regression (GPR) on Mauna Loa CO2 data.