smile.math.kernel

Class Matern

java.lang.Object

smile.math.kernel.Matern

All Implemented Interfaces:

java.io.Serializable, Function, IsotropicKernel

Direct Known Subclasses:

BinarySparseMaternKernel, MaternKernel, SparseMaternKernel

public class Matern
extends java.lang.Object
implements IsotropicKernel

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:

Gaussian, Laplacian, Serialized Form

Constructor Summary

Constructors

Constructor and Description
Matern(double sigma, double nu, double lo, double hi) Constructor.

Method Summary

Modifier and Type	Method and Description
double	f(double dist) Computes the value of the function at x.
double	k(double dist) Computes the isotropic kernel function.
double[]	kg(double dist) Computes the isotropic kernel function and its gradient over hyperparameters..
double	scale() Returns the length scale of kernel.
double	smoothness() Returns the smoothness of kernel.
java.lang.String	toString()

Methods inherited from class java.lang.Object

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

Methods inherited from interface smile.math.kernel.IsotropicKernel

apply, K, KG

Constructor Detail

Matern

public Matern(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 Detail

scale

public double scale()

Returns the length scale of kernel.

smoothness

public double smoothness()

Returns the smoothness of kernel.

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

f

public double f(double dist)

Description copied from interface: Function

Computes the value of the function at x.

Specified by:

f in interface Function

Specified by:

f in interface IsotropicKernel

k

public double k(double dist)

Description copied from interface: IsotropicKernel

Computes the isotropic kernel function.

Specified by:

k in interface IsotropicKernel

Parameters:

dist - The distance.

kg

public double[] kg(double dist)

Description copied from interface: IsotropicKernel

Computes the isotropic kernel function and its gradient over hyperparameters..

Specified by:

kg in interface IsotropicKernel

Parameters:

dist - The distance.