mlpack::distribution::GammaDistribution Class Reference

This class represents the Gamma distribution. More...

#include <gamma_distribution.hpp>

Public Member Functions
	GammaDistribution (const size_t dimensionality=0)
	Construct the Gamma distribution with the given number of dimensions (default 0); each parameter will be initialized to 0. More...
	GammaDistribution (const arma::mat &data, const double tol=1e-8)
	Construct the Gamma distribution, training on the given parameters. More...
	GammaDistribution (const arma::vec &alpha, const arma::vec &beta)
	Construct the Gamma distribution given two vectors alpha and beta. More...
	~GammaDistribution ()
	Destructor.
void	Train (const arma::mat &rdata, const double tol=1e-8)
	This function trains (fits distribution parameters) to new data or the dataset the object owns. More...
void	Train (const arma::mat &observations, const arma::vec &probabilities, const double tol=1e-8)
	Fits an alpha and beta parameter according to observation probabilities. More...
void	Train (const arma::vec &logMeanxVec, const arma::vec &meanLogxVec, const arma::vec &meanxVec, const double tol=1e-8)
	This function trains (fits distribution parameters) to a dataset with pre-computed statistics logMeanx, meanLogx, meanx for each dimension. More...
void	Probability (const arma::mat &observations, arma::vec &probabilities) const
	This function returns the probability of a group of observations. More...
double	Probability (double x, const size_t dim) const
	This is a shortcut to the Probability(arma::mat&, arma::vec&) function for when we want to evaluate only the probability of one dimension of the gamma. More...
void	LogProbability (const arma::mat &observations, arma::vec &logProbabilities) const
	This function returns the logarithm of the probability of a group of observations. More...
double	LogProbability (double x, const size_t dim) const
	This function returns the logarithm of the probability of a single observation. More...
arma::vec	Random () const
	This function returns an observation of this distribution.
double	Alpha (const size_t dim) const
	Get the alpha parameter of the given dimension.
double &	Alpha (const size_t dim)
	Modify the alpha parameter of the given dimension.
double	Beta (const size_t dim) const
	Get the beta parameter of the given dimension.
double &	Beta (const size_t dim)
	Modify the beta parameter of the given dimension.
size_t	Dimensionality () const
	Get the dimensionality of the distribution.

Detailed Description

This class represents the Gamma distribution.

It supports training a Gamma distribution on a given dataset and accessing the fitted alpha and beta parameters.

This class supports multidimensional Gamma distributions; however, it is assumed that each dimension is independent; therefore, a multidimensional Gamma distribution here may be seen as a set of independent single-dimensional Gamma distributions—and the parameters are estimated under this assumption.

The estimation algorithm used can be found in the following paper:

@techreport{minka2002estimating,
  title={Estimating a {G}amma distribution},
  author={Minka, Thomas P.},
  institution={Microsoft Research},
  address={Cambridge, U.K.},
  year={2002}
}

Constructor & Destructor Documentation

GammaDistribution() [1/3]

GammaDistribution::GammaDistribution

(

const size_t

dimensionality = 0

)

Construct the Gamma distribution with the given number of dimensions (default 0); each parameter will be initialized to 0.

Parameters

dimensionality

Number of dimensions.

GammaDistribution() [2/3]

GammaDistribution::GammaDistribution	(	const arma::mat &	data,
		const double	tol = 1e-8
	)

Construct the Gamma distribution, training on the given parameters.

Parameters

data	Data to train the distribution on.
tol	Convergence tolerance. This is not an absolute measure: It will stop the approximation once the change in the value is smaller than tol.

GammaDistribution() [3/3]

GammaDistribution::GammaDistribution	(	const arma::vec &	alpha,
		const arma::vec &	beta
	)

Construct the Gamma distribution given two vectors alpha and beta.

Parameters

alpha	The vector of alphas, one per dimension.
beta	The vector of betas, one per dimension.

Member Function Documentation

LogProbability() [1/2]

void GammaDistribution::LogProbability	(	const arma::mat &	observations,
		arma::vec &	logProbabilities
	)		const

This function returns the logarithm of the probability of a group of observations.

The logarithm of the probability of a value x is

\[ \log(\frac{x^{(\alpha - 1)}}{\Gamma(\alpha) \beta^\alpha} e^ {-\frac{x}{\beta}}) \]

for one dimension. This implementation assumes each dimension is independent, so the product rule is used.

Parameters

observations	Matrix of observations, one per column.
logProbabilities	Column vector of log probabilities, one per observation.

LogProbability() [2/2]

double GammaDistribution::LogProbability	(	double	x,
		const size_t	dim
	)		const

This function returns the logarithm of the probability of a single observation.

Parameters

x	The 1-dimensional observation.
dim	The dimension for which to calculate the probability.

Probability() [1/2]

void GammaDistribution::Probability	(	const arma::mat &	observations,
		arma::vec &	probabilities
	)		const

This function returns the probability of a group of observations.

The probability of the value x is

\[ \frac{x^{(\alpha - 1)}}{\Gamma(\alpha) \beta^\alpha} e^{-\frac{x}{\beta}} \]

for one dimension. This implementation assumes each dimension is independent, so the product rule is used.

Parameters

observations	Matrix of observations, one per column.
probabilities	Column vector of probabilities, one per observation.

Probability() [2/2]

double GammaDistribution::Probability	(	double	x,
		const size_t	dim
	)		const

This is a shortcut to the Probability(arma::mat&, arma::vec&) function for when we want to evaluate only the probability of one dimension of the gamma.

Parameters

x	The 1-dimensional observation.
dim	The dimension for which to calculate the probability.

Train() [1/3]

void GammaDistribution::Train	(	const arma::mat &	rdata,
		const double	tol = 1e-8
	)

This function trains (fits distribution parameters) to new data or the dataset the object owns.

Parameters

rdata	Reference data to fit parameters to.
tol	Convergence tolerance. This is not an absolute measure: It will stop the approximation once the change in the value is smaller than tol.

Train() [2/3]

void GammaDistribution::Train	(	const arma::mat &	observations,
		const arma::vec &	probabilities,
		const double	tol = 1e-8
	)

Fits an alpha and beta parameter according to observation probabilities.

This method is not yet implemented.

Parameters

observations	The reference data, one observation per column.
probabilities	The probability of each observation. One value per column of the observations matrix.
tol	Convergence tolerance. This is not an absolute measure: It will stop the approximation once the change in the value is smaller than tol.

Train() [3/3]

void GammaDistribution::Train	(	const arma::vec &	logMeanxVec,
		const arma::vec &	meanLogxVec,
		const arma::vec &	meanxVec,
		const double	tol = 1e-8
	)

This function trains (fits distribution parameters) to a dataset with pre-computed statistics logMeanx, meanLogx, meanx for each dimension.

Parameters

logMeanxVec	Is each dimension's logarithm of the mean (log(mean(x))).
meanLogxVec	Is each dimension's mean of logarithms (mean(log(x))).
meanxVec	Is each dimension's mean (mean(x)).
tol	Convergence tolerance. This is not an absolute measure: It will stop the approximation once the change in the value is smaller than tol.

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

• src/mlpack/core/dists/gamma_distribution.hpp
• src/mlpack/core/dists/gamma_distribution.cpp