smile.stat.distribution

Class MultivariateGaussianDistribution

java.lang.Object

smile.stat.distribution.AbstractMultivariateDistribution

smile.stat.distribution.MultivariateGaussianDistribution

All Implemented Interfaces:

MultivariateDistribution, MultivariateExponentialFamily

public class MultivariateGaussianDistribution
extends AbstractMultivariateDistribution
implements MultivariateExponentialFamily

Multivariate Gaussian distribution.

See Also:

GaussianDistribution

Constructor Summary

Constructors

Constructor and Description
MultivariateGaussianDistribution(double[][] data) Constructor.
MultivariateGaussianDistribution(double[][] data, boolean diagonal) Constructor.
MultivariateGaussianDistribution(double[] mean, double var) Constructor.
MultivariateGaussianDistribution(double[] mean, double[] var) Constructor.
MultivariateGaussianDistribution(double[] mean, double[][] cov) Constructor.

Method Summary

Modifier and Type	Method and Description
double	cdf(double[] x) Algorithm from Alan Genz (1992) Numerical Computation of Multivariate Normal Probabilities, Journal of Computational and Graphical Statistics, pp.
double[][]	cov() The covariance matrix of distribution.
double	entropy() Shannon entropy of the distribution.
boolean	isDiagonal() Returns true if the covariance matrix is diagonal.
double	logp(double[] x) The density at x in log scale, which may prevents the underflow problem.
MultivariateMixture.Component	M(double[][] x, double[] posteriori) The M step in the EM algorithm, which depends the specific distribution.
double[]	mean() The mean vector of distribution.
int	npara() The number of parameters of the distribution.
double	p(double[] x) The probability density function for continuous distribution or probability mass function for discrete distribution at x.
double[]	rand() Generate a random multivariate Gaussian sample.
double	scatter() Returns the scatter of distribution, which is defined as |Σ|.
java.lang.String	toString()

Methods inherited from class smile.stat.distribution.AbstractMultivariateDistribution

likelihood, logLikelihood

Methods inherited from class java.lang.Object

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

Constructor Detail

MultivariateGaussianDistribution

public MultivariateGaussianDistribution(double[] mean,
                                        double var)

Constructor. The distribution will have a diagonal covariance matrix of the same variance.

Parameters:

mean - mean vector.

var - variance.

MultivariateGaussianDistribution

public MultivariateGaussianDistribution(double[] mean,
                                        double[] var)

Constructor. The distribution will have a diagonal covariance matrix. Each element has different variance.

Parameters:

mean - mean vector.

var - variance vector.

MultivariateGaussianDistribution

public MultivariateGaussianDistribution(double[] mean,
                                        double[][] cov)

Constructor.

Parameters:

mean - mean vector.

cov - covariance matrix.

MultivariateGaussianDistribution

public MultivariateGaussianDistribution(double[][] data)

Constructor. Mean and covariance will be estimated from the data by MLE.

Parameters:

data - the training data.

MultivariateGaussianDistribution

public MultivariateGaussianDistribution(double[][] data,
                                        boolean diagonal)

Constructor. Mean and covariance will be estimated from the data by MLE.

Parameters:

data - the training data.

diagonal - true if covariance matrix is diagonal.

Method Detail

isDiagonal

public boolean isDiagonal()

Returns true if the covariance matrix is diagonal.

Returns:

true if the covariance matrix is diagonal

npara

public int npara()

Description copied from interface: MultivariateDistribution

The number of parameters of the distribution.

Specified by:

npara in interface MultivariateDistribution

entropy

public double entropy()

Description copied from interface: MultivariateDistribution

Shannon entropy of the distribution.

Specified by:

entropy in interface MultivariateDistribution

mean

public double[] mean()

Description copied from interface: MultivariateDistribution

The mean vector of distribution.

Specified by:

mean in interface MultivariateDistribution

cov

public double[][] cov()

Description copied from interface: MultivariateDistribution

The covariance matrix of distribution.

Specified by:

cov in interface MultivariateDistribution

scatter

public double scatter()

Returns the scatter of distribution, which is defined as |Σ|.

logp

public double logp(double[] x)

Description copied from interface: MultivariateDistribution

The density at x in log scale, which may prevents the underflow problem.

Specified by:

logp in interface MultivariateDistribution

p

public double p(double[] x)

Description copied from interface: MultivariateDistribution

The probability density function for continuous distribution or probability mass function for discrete distribution at x.

Specified by:

p in interface MultivariateDistribution

cdf

public double cdf(double[] x)

Algorithm from Alan Genz (1992) Numerical Computation of Multivariate Normal Probabilities, Journal of Computational and Graphical Statistics, pp. 141-149. The difference between returned value and the true value of the CDF is less than 0.001 in 99.9% time. The maximum number of iterations is set to 10000.

Specified by:

cdf in interface MultivariateDistribution

rand

public double[] rand()

Generate a random multivariate Gaussian sample.

M

public MultivariateMixture.Component M(double[][] x,
                                       double[] posteriori)

Description copied from interface: MultivariateExponentialFamily

The M step in the EM algorithm, which depends the specific distribution.

Specified by:

M in interface MultivariateExponentialFamily

Parameters:

x - the input data for estimation

posteriori - the posteriori probability.

Returns:

the (unnormalized) weight of this distribution in the mixture.

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object