bdm::MixEF Class Reference

Mixture of Exponential Family Densities. More...

#include <mixef.h>

Inheritance diagram for bdm::MixEF:

Collaboration diagram for bdm::MixEF:

List of all members.

Public Member Functions

MixEF (const Array< BMEF * > &Coms0, const vec &alpha0)

Full constructor.

MixEF ()

Constructor of empty mixture.

MixEF (const MixEF &M2)

Copy constructor.

void init (BMEF *Com0, const mat &Data, int c=5)

void bayes (const vec &dt)

Recursive EM-like algorithm (QB-variant), see Karny et. al, 2006.

void bayes (const mat &dt)

EM algorithm.

void bayesB (const mat &dt, const vec &wData)

double logpred (const vec &dt) const

const epdf & _epdf () const

Returns a reference to the epdf representing posterior density on parameters.

const eprod * _e () const

Returns a pointer to the epdf representing posterior density on parameters. Use with care!

emix * predictor (const RV &rv) const

Constructs a predictive density (marginal density on data).

void flatten (const BMEF *M2)

Flatten the density as if it was not estimated from the data.

BMEF * _Coms (int i)

Access function.

void set_method (MixEF_METHOD M)

Set which method is to be used.

virtual void set_statistics (const BMEF *BM0)

get statistics from another model

virtual void bayes (const vec &data, const double w)

Weighted update of sufficient statistics (Bayes rule).

BMEF * _copy_ (bool changerv=false)

Flatten the posterior as if to keep nu0 data.

virtual void bayesB (const mat &Dt)

Batch Bayes rule (columns of Dt are observations).

vec logpred_m (const mat &dt) const

Matrix version of logpred.

const RV & _rv () const

access function

double _ll () const

access function

void set_evalll (bool evl0)

access function

Protected Member Functions

void build_est ()

Auxiliary function for use in constructors.

Protected Attributes

int n

Number of components.

Array< BMEF * > Coms

Models for Components of $\theta_i$ .

multiBM weights

Statistics for weights.

eprod * est

Posterior on component parameters.

MixEF_METHOD method

Flag for a method that is used in the inference.

double frg

forgetting factor

double last_lognc

cached value of lognc() in the previous step (used in evaluation of ll )

RV rv

Random variable of the posterior.

double ll

Logarithm of marginalized data likelihood.

bool evalll

If true, the filter will compute likelihood of the data record and store it in ll . Set to false if you want to save computational time.

Detailed Description

Mixture of Exponential Family Densities.

An approximate estimation method for models with latent discrete variable, such as mixture models of the following kind:

$f(y_t|\psi_t, \Theta) = \sum_{i=1}^{n} w_i f(y_t|\psi_t, \theta_i)$

where $\psi$ is a known function of past outputs, $w=[w_1,\ldots,w_n]$ are component weights, and component parameters $\theta_i$ are assumed to be mutually independent. $\Theta$ is an aggregation af all component parameters and weights, i.e. $\Theta = [\theta_1,\ldots,\theta_n,w]$ .

The characteristic feature of this model is that if the exact values of the latent variable were known, estimation of the parameters can be handled by a single model. For example, for the case of mixture models, posterior density for each component parameters would be a BayesianModel from Exponential Family.

This class uses EM-style type algorithms for estimation of its parameters. Under this simplification, the posterior density is a product of exponential family members, hence under EM-style approximate estimation this class itself belongs to the exponential family.

TODO: Extend BM to use rvc.

Member Function Documentation

void bdm::MixEF::init	(	BMEF *	Com0,
		const mat &	Data,
		int	c = `5`
	)

Initializing the mixture by a random pick of centroids from data

Parameters:

	Com0	Initial component - necessary to determine its type.
	Data	Data on which the initialization will be done
	c	Initial number of components, default=5

References bdm::BMEF::_copy_(), build_est(), Coms, est, n, bdm::multiBM::set_parameters(), and weights.

Referenced by bdm::merger::merge().

double bdm::MixEF::logpred ( const vec & dt ) const [virtual]

Evaluates predictive log-likelihood of the given data record I.e. marginal likelihood of the data with the posterior integrated out.

Reimplemented from bdm::BM.

References bdm::multiBM::_epdf(), Coms, bdm::epdf::mean(), and weights.

Referenced by bdm::merger::evallog(), and bdm::merger::merge().

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

work/git/mixpp/bdm/estim/mixef.h
work/git/mixpp/bdm/estim/mixef.cpp


Public Member Functions
	MixEF (const Array< BMEF * > &Coms0, const vec &alpha0)
	Full constructor.
	MixEF ()
	Constructor of empty mixture.
	MixEF (const MixEF &M2)
	Copy constructor.
void	init (BMEF *Com0, const mat &Data, int c=5)
void	bayes (const vec &dt)
	Recursive EM-like algorithm (QB-variant), see Karny et. al, 2006.
void	bayes (const mat &dt)
	EM algorithm.
void	bayesB (const mat &dt, const vec &wData)
double	logpred (const vec &dt) const
const epdf &	_epdf () const
	Returns a reference to the epdf representing posterior density on parameters.
const eprod *	_e () const
	Returns a pointer to the epdf representing posterior density on parameters. Use with care!
emix *	predictor (const RV &rv) const
	Constructs a predictive density (marginal density on data).
void	flatten (const BMEF *M2)
	Flatten the density as if it was not estimated from the data.
BMEF *	_Coms (int i)
	Access function.
void	set_method (MixEF_METHOD M)
	Set which method is to be used.
virtual void	set_statistics (const BMEF *BM0)
	get statistics from another model
virtual void	bayes (const vec &data, const double w)
	Weighted update of sufficient statistics (Bayes rule).
BMEF *	_copy_ (bool changerv=false)
	Flatten the posterior as if to keep nu0 data.
virtual void	bayesB (const mat &Dt)
	Batch Bayes rule (columns of Dt are observations).
vec	logpred_m (const mat &dt) const
	Matrix version of logpred.
const RV &	_rv () const
	access function
double	_ll () const
	access function
void	set_evalll (bool evl0)
	access function
Protected Member Functions
void	build_est ()
	Auxiliary function for use in constructors.
Protected Attributes
int	n
	Number of components.
Array< BMEF * >	Coms
	Models for Components of $\theta_i$ .
multiBM	weights
	Statistics for weights.
eprod *	est
	Posterior on component parameters.
MixEF_METHOD	method
	Flag for a method that is used in the inference.
double	frg
	forgetting factor
double	last_lognc
	cached value of lognc() in the previous step (used in evaluation of `ll` )
RV	rv
	Random variable of the posterior.
double	ll
	Logarithm of marginalized data likelihood.
bool	evalll
	If true, the filter will compute likelihood of the data record and store it in `ll` . Set to false if you want to save computational time.