Source code for infpy.gp.rational_quadratic_kernel

#
# Copyright John Reid 2006
#


from real_kernel import *
import numpy, math

class RationalQuadraticKernel( RealKernel ):
    """
    Following 4.19 in `Gaussian Processes for Machine Learning`__ by Rasmussen and Williams. 

    __ http://www.amazon.co.uk/Gaussian-Processes-Learning-Adaptive-Computation/dp/026218253X/

    .. math::
        
        k = (1 + \\frac{r^2}{2\\alpha})^{-\\alpha}

    Alpha is not a trainable parameter.
    The parameters are for the length scale in the r term.
    """

    def __init__(
            self,
            alpha,
            params = None,
            priors = None,
            dimensions = None
    ):
        self.alpha = alpha
        ( params, priors, dimensions ) = kernel_init_args_helper(
                params,
                priors,
                dimensions
        )
        RealKernel.__init__(
                self,
                params,
                priors,
                dimensions
        )

    def __str__( self ):
        return """RQKernelFixedAlpha( alpha = %f )""" % self.alpha

    def __call__( self, x1, x2, identical = False ):
        (x1, x2) = self._check_args( x1, x2 )
        r2 = distance_2( x1, x2, self.params )
        return ( 1.0 + r2 / ( 2.0 * self.alpha ) ) ** (-self.alpha)

    class Derivative( object ):
        def __init__( self, k, i ):
            self.k = k
            self.i = i
        def __call__( self, x1, x2, identical = False ):
            (x1, x2) = self.k._check_args( x1, x2 )
            r2 = distance_2( x1, x2, self.k.params )
            term = 1.0 + r2 / ( 2.0 * self.k.alpha )
            return -(
                    term ** (-self.k.alpha-1.0)
                    / 2.0
            ) * distance_2_derivative( x1, x2, self.k.params, self.i )




class RationalQuadraticKernelAlphaParameterised( RealKernel ):
    """Following 4.19 in `Gaussian Processes for Machine Learning`__ by Rasmussen and Williams. 

    __ http://www.amazon.co.uk/Gaussian-Processes-Learning-Adaptive-Computation/dp/026218253X/

    .. math::
        
        k = (1 + \\frac{r^2}{2\\alpha})^{-\\alpha}

    The first parameter is alpha.
    The rest of the parameters are for the length scale in the r term.
    """

    def __init__(
            self,
            params = None,
            priors = None,
            dimensions = None
    ):
        ( params, priors, dimensions ) = kernel_init_args_helper(
                params,
                priors,
                dimensions,
                num_extra_params = 1
        )
        RealKernel.__init__(
                self,
                params,
                priors,
                dimensions
        )

    def alpha( self ): return self.params[0]

    def __call__( self, x1, x2, identical = False ):
        (x1, x2) = self._check_args( x1, x2 )
        r2 = distance_2( x1, x2, self.params[1:] )
        return ( 1.0 + r2 / ( 2.0 * self.alpha() ) ) ** (-self.alpha())

    def __str__( self ):
        return """RQKernelAlphaParameterised( alpha = %f )""" % self.alpha()

    class Derivative( object ):
        def __init__( self, k, i ):
            self.k = k
            self.i = i
        def __call__( self, x1, x2, identical = False ):
            (x1, x2) = self.k._check_args( x1, x2 )
            r2 = distance_2( x1, x2, self.k.params[1:] )
            term = 1.0 + r2 / ( 2.0 * self.k.alpha() )
            if self.i == 0: # alpha
                return (
                        -2.0 * self.k.alpha() * math.log( term ) * term ** (-self.k.alpha())
                        + r2 * term ** (-self.k.alpha() - 1)
                ) / (
                        2 * self.k.alpha()
                )
            else: # lengthscale
                return -(
                        term ** (-self.k.alpha()-1.0)
                        / 2.0
                ) * distance_2_derivative( x1, x2, self.k.params[1:], self.i - 1 )