sklearn.gaussian_process.kernels.ExpSineSquared  
class sklearn.gaussian_process.kernels.ExpSineSquared(length_scale=1.0, periodicity=1.0, length_scale_bounds=1e-05, 100000.0, periodicity_bounds=1e-05, 100000.0) [source]
 
Exp-Sine-Squared kernel (aka periodic kernel). The ExpSineSquared kernel allows one to model functions which repeat themselves exactly. It is parameterized by a length scale parameter \(l>0\) and a periodicity parameter \(p>0\). Only the isotropic variant where \(l\) is a scalar is supported at the moment. The kernel is given by:  \[k(x_i, x_j) = \text{exp}\left(- \frac{ 2\sin^2(\pi d(x_i, x_j)/p) }{ l^ 2} \right)\] where \(l\) is the length scale of the kernel, \(p\) the periodicity of the kernel and \(d(\\cdot,\\cdot)\) is the Euclidean distance. Read more in the User Guide.  New in version 0.18.   Parameters 
 
length_scalefloat > 0, default=1.0 

The length scale of the kernel.  
periodicityfloat > 0, default=1.0 

The periodicity of the kernel.  
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.  
periodicity_boundspair of floats >= 0 or “fixed”, default=(1e-5, 1e5) 

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


Returns the log-transformed bounds on the theta.  
hyperparameter_length_scale


Returns the length scale  hyperparameter_periodicity

hyperparameters


Returns a list of all hyperparameter specifications.  
n_dims


Returns the number of non-fixed hyperparameters of the kernel.  
requires_vector_input


Returns whether the kernel is defined on fixed-length feature vectors or generic objects.  
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 ExpSineSquared
>>> X, y = make_friedman2(n_samples=50, noise=0, random_state=0)
>>> kernel = ExpSineSquared(length_scale=1, periodicity=1)
>>> gpr = GaussianProcessRegressor(kernel=kernel, alpha=5,
...         random_state=0).fit(X, y)
>>> gpr.score(X, y)
0.0144...
>>> gpr.predict(X[:2,:], return_std=True)
(array([425.6..., 457.5...]), array([0.3894..., 0.3467...]))
 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 
 
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), 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 
 
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 hyperparameter_length_scale  
Returns the length scale 
  
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  
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     
 
 Examples using sklearn.gaussian_process.kernels.ExpSineSquared
 
  Comparison of kernel ridge and Gaussian process regression  

  Illustration of prior and posterior Gaussian process for different kernels  

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