org.knowceans.util
Class Densities

java.lang.Object
  org.knowceans.util.Densities

public class Densities
extends java.lang.Object

Densities calculates for different density functions the likelihood of a data item given the parameters

Author:

heinrich

Constructor Summary

Densities()

Method Summary

static double	pdfBeta(double x, double a, double b) beta likelihood
static double	pdfBinomial(int n, int N, double p) Binom(n | N, p) using linear binomial coefficient
static double	pdfDirichlet(double[] xx, double alpha) Symmetric Dirichlet likelihood:
static double	pdfDirichlet(double[] xx, double[] alpha) Dirichlet likelihood using logarithmic calculation
static double	pdfDirichlet(double[] xx, double[] basemeasure, double precision) Dirichlet likelihood using logarithmic calculation
static double	pdfDmm(double[] xx, double[] probs, double[][] parameters) Dirichlet mixture likelihood using Dirichlet parameters and assuming independence between components.
static double	pdfDmm(double[] x, double[] probs, double[][] basemeasure, double[] precision) Dirichlet mixture likelihood using mean and precision
static double	pdfGamma(double x, double a, double b) gamma likelihood p(x|a,b) = x^(a-1) * e^(-x/b) / (b^a * Gamma(a))
static double	pdfGmm(double x, double[] probs, double[] mean, double[] sigma) GMM likelihood
static double	pdfMultinomial(int[] nn, double[] pp) Mult(nn|pp) using logarithmic multinomial coefficient
static double	pdfNorm(double x, double mu, double sigma) Normal likelihood

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Densities

public Densities()

Method Detail

pdfNorm

public static double pdfNorm(double x,
                             double mu,
                             double sigma)

Normal likelihood

Parameters:

x -

mu -

sigma -

Returns:

pdfGmm

public static double pdfGmm(double x,
                            double[] probs,
                            double[] mean,
                            double[] sigma)

GMM likelihood

Parameters:

x -

k -

probs -

mean -

sigma -

Returns:

pdfDmm

public static double pdfDmm(double[] x,
                            double[] probs,
                            double[][] basemeasure,
                            double[] precision)

Dirichlet mixture likelihood using mean and precision

Parameters:

x -

probs -

basemeasure - -- multinomial parameter around which the distribution scatters, m = alpha / s

precision - -- s = sum alpha

Returns:

pdfDmm

public static double pdfDmm(double[] xx,
                            double[] probs,
                            double[][] parameters)

Dirichlet mixture likelihood using Dirichlet parameters and assuming independence between components.

Parameters:

x -

k -

probs -

mean -

precision -

Returns:

pdfGamma

public static double pdfGamma(double x,
                              double a,
                              double b)

gamma likelihood p(x|a,b) = x^(a-1) * e^(-x/b) / (b^a * Gamma(a))

Parameters:

x - value

a - (shape?)

b - (scale?)

Returns:

pdfBeta

public static double pdfBeta(double x,
                             double a,
                             double b)

beta likelihood

Parameters:

x - data item

a - pseudo counts for success

b - pseudo counts for failure

Returns:

pdfDirichlet

public static double pdfDirichlet(double[] xx,
                                  double[] alpha)

Dirichlet likelihood using logarithmic calculation

Dir(xx|alpha) =

Gamma(sum_i alpha[i])/(prod_i Gamma(alpha[i])) prod_i xx[i]^(alpha[i]-1)

Parameters:

xx - multivariate convex data item (sum=1)

alpha - Dirichlet parameter vector

Returns:

pdfDirichlet

public static double pdfDirichlet(double[] xx,
                                  double[] basemeasure,
                                  double precision)

Dirichlet likelihood using logarithmic calculation

Dir(xx|alpha) =

Gamma(sum_i alpha[i])/(prod_i Gamma(alpha[i])) prod_i xx[i]^(alpha[i]-1)

Parameters:

xx - multivariate convex data item (sum=1)

basemeasure - -- normalised coefficients (= mean)

precision - -- central moment ...

Returns:

pdfDirichlet

public static double pdfDirichlet(double[] xx,
                                  double alpha)

Symmetric Dirichlet likelihood:

Dir(xx|alpha) = Gamma(k * alpha)/Gamma(alpha)^k prod_i xx[i]^(alpha - 1)

Parameters:

xx - multivariate convex data item (sum=1)

alpha - symmetric parameter

Returns:

pdfMultinomial

public static double pdfMultinomial(int[] nn,
                                    double[] pp)

Mult(nn|pp) using logarithmic multinomial coefficient

Parameters:

nn - counts for each category

pp - convex probability vector for categories

Returns:

pdfBinomial

public static double pdfBinomial(int n,
                                 int N,
                                 double p)

Binom(n | N, p) using linear binomial coefficient

Parameters:

n -

N -

p -

Returns: