surrogate.kernels

surrogate.kernels

Classes

Name	Description
ConstantKernel	Constant kernel.
Kernel	Base class for Kernels.
Product	The Product kernel k1 * k2.
RBF	Radial Basis Function (RBF) kernel.
SpotOptimKernel	Kernel designed for SpotOptim’s Kriging with mixed variable support.
Sum	The Sum kernel k1 + k2.
WhiteKernel	White kernel.

ConstantKernel

surrogate.kernels.ConstantKernel(
    constant_value=1.0,
    constant_value_bounds=(1e-05, 100000.0),
)

Constant kernel.

Can be used as a scaling factor (e.g. 2.0 * RBF()) or as part of a sum (e.g. RBF() + 1.0).

Parameters

Name	Type	Description	Default
constant_value	float	The constant value. Defaults to 1.0.	1.0
constant_value_bounds	tuple	The lower and upper bound on constant_value. Defaults to (1e-5, 1e5).	(1e-05, 100000.0)

Kernel

surrogate.kernels.Kernel()

Base class for Kernels.

Methods

Name	Description
diag	Returns the diagonal of the kernel k(X, X).

diag

surrogate.kernels.Kernel.diag(X)

Returns the diagonal of the kernel k(X, X).

The result of this method is equivalent to np.diag(self(X)); however, it can be evaluated more efficiently.

Parameters

Name	Type	Description	Default
X	np.ndarray	Argument of the kernel evaluation.	required

Returns

Name	Type	Description
	np.ndarray	np.ndarray: Diagonal of the kernel matrix, shape (n_samples_X,).

Product

surrogate.kernels.Product(k1, k2)

The Product kernel k1 * k2.

The kernel value is k1(X, Y) * k2(X, Y).

Parameters

Name	Type	Description	Default
k1	Kernel	First kernel.	required
k2	Kernel	Second kernel.	required

RBF

surrogate.kernels.RBF(length_scale=1.0, length_scale_bounds=(1e-05, 100000.0))

Radial Basis Function (RBF) kernel.

Also known as the “squared exponential” kernel. It is given by: k(x_i, x_j) = exp(-0.5 * d(x_i, x_j)^2 / length_scale^2)

Parameters

Name	Type	Description	Default
length_scale	float or np.ndarray	The length scale of the kernel. If a float, using isotropic distances. If an array, using anisotropic distances. Defaults to 1.0.	1.0
length_scale_bounds	tuple	The lower and upper bound on length_scale. Defaults to (1e-5, 1e5).	(1e-05, 100000.0)

SpotOptimKernel

surrogate.kernels.SpotOptimKernel(
    theta,
    var_type,
    p_val=2.0,
    metric_factorial='canberra',
)

Kernel designed for SpotOptim’s Kriging with mixed variable support.

It handles continuous (‘float’), integer (‘int’), and categorical (‘factor’) variables similarly to the internal logic of the Kriging class.

The correlation function is defined as: Psi = exp(- (D_ordered + D_factor))

where: D_ordered = sum_j theta_j * |x_ij - y_lj|^p (for ordered variables) D_factor = sum_j theta_j * d(x_ij, y_lj) (for factor variables, d is metric like Canberra)

Parameters

Name	Type	Description	Default
theta	np.ndarray	The correlation parameters (weights). Note: In standard Kriging usage, this corresponds to 10^theta_log. This kernel expects the LINEAR scale theta values (weights), not log.	required
var_type	list of str	List of variable types, e.g. [‘float’, ‘int’, ‘factor’].	required
p_val	float	Power parameter for ordered distance. Defaults to 2.0.	2.0
metric_factorial	str	Metric for factor distance (passed to cdist/pdist). Defaults to ‘canberra’.	'canberra'

Sum

surrogate.kernels.Sum(k1, k2)

The Sum kernel k1 + k2.

The kernel value is k1(X, Y) + k2(X, Y).

Parameters

Name	Type	Description	Default
k1	Kernel	First kernel.	required
k2	Kernel	Second kernel.	required

WhiteKernel

surrogate.kernels.WhiteKernel(
    noise_level=1.0,
    noise_level_bounds=(1e-05, 100000.0),
)

White kernel.

The main use case is capturing noise in the signal: k(x_i, x_j) = noise_level if x_i == x_j else 0

Parameters

Name	Type	Description	Default
noise_level	float	Parameter controlling the noise level (variance). Defaults to 1.0.	1.0
noise_level_bounds	tuple	The lower and upper bound on noise_level. Defaults to (1e-5, 1e5).	(1e-05, 100000.0)