smile.math.kernel

Class MaternKernel

java.lang.Object

smile.math.kernel.Matern

smile.math.kernel.MaternKernel

All Implemented Interfaces:

java.io.Serializable, java.util.function.ToDoubleBiFunction<double[],double[]>, Function, IsotropicKernel, MercerKernel<double[]>

public class MaternKernel
extends Matern
implements MercerKernel<double[]>

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:

GaussianKernel, LaplacianKernel, Serialized Form

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
double[]	hi() Returns the upper bound of hyperparameters.
double[]	hyperparameters() Returns the hyperparameters for tuning.
double	k(double[] x, double[] y) Kernel function.
double[]	kg(double[] x, double[] y) Computes the kernel and its gradient over hyperparameters.
double[]	lo() Returns the lower bound of hyperparameters.
MaternKernel	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.kernel.MercerKernel

apply, applyAsDouble, K, K, KG

Methods inherited from interface smile.math.kernel.IsotropicKernel

apply, K, KG

Constructor Detail

MaternKernel

public MaternKernel(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.

MaternKernel

public MaternKernel(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

k

public double k(double[] x,
                double[] y)

Description copied from interface: MercerKernel

Kernel function.

Specified by:

k in interface MercerKernel<double[]>

kg

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

Description copied from interface: MercerKernel

Computes the kernel and its gradient over hyperparameters.

Specified by:

kg in interface MercerKernel<double[]>

of

public MaternKernel of(double[] params)

Description copied from interface: MercerKernel

Returns the same kind kernel with the new hyperparameters.

Specified by:

of in interface MercerKernel<double[]>

hyperparameters

public double[] hyperparameters()

Description copied from interface: MercerKernel

Returns the hyperparameters for tuning.

Specified by:

hyperparameters in interface MercerKernel<double[]>

lo

public double[] lo()

Description copied from interface: MercerKernel

Returns the lower bound of hyperparameters.

Specified by:

lo in interface MercerKernel<double[]>

hi

public double[] hi()

Description copied from interface: MercerKernel

Returns the upper bound of hyperparameters.

Specified by:

hi in interface MercerKernel<double[]>