Package smile.math.kernel

Class SparseMaternKernel

java.lang.Object

smile.math.kernel.Matern

smile.math.kernel.SparseMaternKernel

All Implemented Interfaces:

Serializable, ToDoubleBiFunction<SparseArray,SparseArray>, Function, IsotropicKernel, MercerKernel<SparseArray>

public class SparseMaternKernel
extends Matern
implements MercerKernel<SparseArray>

The class of Matérn kernels is a generalization of the Gaussian/RBF. It has an additional parameter nu which controls the smoothness of the kernel function. The smaller nu, the less smooth the approximated function is. As nu -> inf, the kernel becomes equivalent to the Gaussian/RBF kernel. When nu = 1/2, the kernel becomes identical to the Laplacian kernel. The Matern kernel become especially simple when nu is half-integer. Important intermediate values are 3/2 (once differentiable functions) and 5/2 (twice differentiable functions).

See Also:

• SparseGaussianKernel
• SparseLaplacianKernel
• Serialized Form

Constructor Summary

Constructors

Constructor	Description
SparseMaternKernel(double sigma, double nu)	Constructor.
SparseMaternKernel(double sigma, double nu, double lo, double hi)	Constructor.

Method Summary

Modifier and Type	Method	Description
double[]	hi()	Returns the upper bound of hyperparameters (in hyperparameter tuning).
double[]	hyperparameters()	Returns the hyperparameters of kernel.
double	k(SparseArray x, SparseArray y)	Kernel function.
double[]	kg(SparseArray x, SparseArray y)	Computes the kernel and its gradient over hyperparameters.
double[]	lo()	Returns the lower bound of hyperparameters (in hyperparameter tuning).
SparseMaternKernel	of(double[] params)	Returns the same kind kernel with the new hyperparameters.

Methods inherited from class smile.math.kernel.Matern

f, k, kg, scale, smoothness, toString

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface smile.math.Function

inv

Methods inherited from interface smile.math.kernel.IsotropicKernel

apply, K, KG

Methods inherited from interface smile.math.kernel.MercerKernel

apply, applyAsDouble, K, K, KG

Constructor Details

SparseMaternKernel

public SparseMaternKernel(double sigma,
 double nu)

Constructor.

Parameters:

sigma - The length scale of kernel.

nu - The smoothness of the kernel function. Only 0.5, 1.5, 2.5 and Inf are accepted.

SparseMaternKernel

public SparseMaternKernel(double sigma,
 double nu,
 double lo,
 double hi)

Constructor.

Parameters:

sigma - The length scale of kernel.

nu - The smoothness of the kernel function. Only 0.5, 1.5, 2.5 and Inf are accepted. The smoothness parameter is fixed during hyperparameter for tuning.

lo - The lower bound of length scale for hyperparameter tuning.

hi - The upper bound of length scale for hyperparameter tuning.

Method Details

k

public double k(SparseArray x,
 SparseArray y)

Description copied from interface: MercerKernel

Kernel function.

Specified by:

k in interface MercerKernel<SparseArray>

Parameters:

x - an object.

y - an object.

Returns:

the kernel value.

kg

public double[] kg(SparseArray x,
 SparseArray y)

Description copied from interface: MercerKernel

Computes the kernel and its gradient over hyperparameters.

Specified by:

kg in interface MercerKernel<SparseArray>

Parameters:

x - an object.

y - an object.

Returns:

the kernel value and gradient.

of

public SparseMaternKernel of(double[] params)

Description copied from interface: MercerKernel

Returns the same kind kernel with the new hyperparameters.

Specified by:

of in interface MercerKernel<SparseArray>

Parameters:

params - the hyperparameters.

Returns:

the same kind kernel with the new hyperparameters.

hyperparameters

public double[] hyperparameters()

Description copied from interface: MercerKernel

Returns the hyperparameters of kernel.

Specified by:

hyperparameters in interface MercerKernel<SparseArray>

Returns:

the hyperparameters of kernel.

lo

public double[] lo()

Description copied from interface: MercerKernel

Returns the lower bound of hyperparameters (in hyperparameter tuning).

Specified by:

lo in interface MercerKernel<SparseArray>

Returns:

the lower bound of hyperparameters.

hi

public double[] hi()

Description copied from interface: MercerKernel

Returns the upper bound of hyperparameters (in hyperparameter tuning).

Specified by:

hi in interface MercerKernel<SparseArray>

Returns:

the upper bound of hyperparameters.