Multivariate gaussian N(mu,K) of d dimensions. More...

#include <gaussian.h>

Public Types
typedef Gaussian< T >	MyT

typedef VectorTemplate< T >	VectorT

typedef MatrixTemplate< T >	MatrixT

Public Member Functions
	Gaussian (int d)

	Gaussian (const MatrixT &sigma, const VectorT &mu)

	Gaussian (const MyT &g)

void	resize (int d)

int	numDims () const

int	degeneracy () const

Real	normalizationFactor () const

bool	setCovariance (const MatrixT &sigma, int verbose=1)
	Covariance matrix must be symmetric, strictly positive definite.

void	getCovariance (MatrixT &sigma) const

void	getVariance (VectorT &sigma) const

void	getPrecision (MatrixT &sigma) const

void	setMean (const VectorT &mu)

const VectorT &	getMean () const

bool	setMaximumLikelihood (const std::vector< VectorT > &examples, int verbose=1)
	ML estimation.

bool	setMaximumLikelihood (const std::vector< VectorT > &examples, const std::vector< Real > &weights, int verbose=1)

void	setMaximumLikelihoodDiagonal (const std::vector< VectorT > &examples)

void	setMaximumLikelihoodDiagonal (const std::vector< VectorT > &examples, const std::vector< Real > &weights)

bool	setMaximumAPosteriori (const std::vector< VectorT > &examples, const VectorT &meanprior, T meanStrength, const MatrixT &covprior, T covStrength, int verbose=1)
	MAP estimation with inverse weishart distribution.

bool	setMaximumAPosteriori (const std::vector< VectorT > &examples, const std::vector< Real > &weights, const VectorT &meanprior, T meanStrength, const MatrixT &covprior, T covStrength, int verbose=1)

void	setMaximumAPosterioriDiagonal (const std::vector< VectorT > &examples, const VectorT &meanprior, T meanStrength, const VectorT &varprior, T covStrength)

void	setMaximumAPosterioriDiagonal (const std::vector< VectorT > &examples, const std::vector< Real > &weights, const VectorT &meanprior, T meanStrength, const VectorT &varprior, T covStrength)

T	probability (const VectorT &x) const
	Evaluates the probability of x.

T	logProbability (const VectorT &x) const
	Evaluates the log-probability of x.

T	partialProbability (const VectorT &x, const std::vector< int > &elements) const
	Evaluates the probability of a partial setting x(elements[i])=x[i].

T	logPartialProbability (const VectorT &x, const std::vector< int > &elements) const
	Evaluates the log partial probability.

void	generate (VectorT &x) const
	Generates a point x according to this distribution.

void	setJoint (const MyT &g1, const MyT &g2)

void	setJoint (const MyT &g1, const MyT &g2, const MatrixT &corr)

void	setMarginalized (const MyT &g, int i)

void	setMarginalized (const MyT &g, const std::vector< int > &elements)

void	setConditional (const MyT &g, Real xi, int i)

void	setConditional (const MyT &g, const VectorT &x, const std::vector< int > &elements)

T	klDivergence (const MyT &g) const

Public Attributes
MatrixT	L
	Cholesky decomposition of the covariance matrix.

VectorT	mu
	mean

Detailed Description

template<class T>
class Math::Gaussian< T >

Multivariate gaussian N(mu,K) of d dimensions.

$P(x~N(mu,K)) = c e^{-1/2 (x-mu)^t K^{-1} (x-mu))}$ where c = 1/sqrt((2pi)^d |K|).

Represented by the cholesky decomposition of K = LL^t.

$x^t K^{-1} x = x^t (L L^t)^{-1} x = x^t L^{-t} L^{-1} x = |L^{-1} x|^2$

so sqrt(|K|) = |L| = product of diag(L). Equivalent to the change of variable y = L^-1(x-mu), such that P(x~N(mu,K)) = P(y~N(0,I))

The documentation for this class was generated from the following files:

gaussian.h
gaussian.cpp

Public Types

Public Member Functions

Public Attributes

Detailed Description

template<class T> class Math::Gaussian< T >

template<class T>
class Math::Gaussian< T >