bdm::MixEF Class Reference

#include <mixef.h>

Inheritance diagram for bdm::MixEF:

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.

Extension to conditional BM

This extension is useful e.g. in Marginalized Particle Filter (bdm::MPF). Alternatively, it can be used for automated connection to DS when the condition is observed

const RV & _rvc () const

access function

virtual void condition (const vec &val)

Substitute val for rvc.

RV rvc

Name of extension variable.

Logging of results

void set_options (const string &opt)

Set boolean options from a string.

void log_add (logger *L, const string &name="")

Add all logged variables to a logger.

void logit (logger *L)

ivec LIDs

IDs of storages in loggers.

bool opt_L_bounds

Option for logging bounds.

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 & posterior () const

const eprod * _e () const

emix * epredictor () const

Constructs a predictive density $f(d_{t+1} |d_{t}, \ldots d_{0})$ .

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) const

Flatten the posterior as if to keep nu0 data.

Constructors

virtual BM * _copy_ () const

Mathematical operations

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.

virtual mpdf * predictor () const

Constructs a conditional density 1-step ahead predictor.

Access to attributes

const RV & _drv () const

void set_drv (const RV &rv)

void set_rv (const RV &rv)

double _ll () const

void set_evalll (bool evl0)

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 drv

Random variable of the data (optional).

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.

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

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

virtual BM* bdm::BM::_copy_ ( ) const [inline, virtual, inherited]

Copy function required in vectors, Arrays of BM etc. Have to be DELETED manually! Prototype:

 BM* _copy_() const {return new BM(*this);}

Reimplemented in bdm::ARX, bdm::KalmanCh, bdm::EKF< sq_T >, and bdm::EKFCh.

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

mixef.h
mixef.cpp


Extension to conditional BM
This extension is useful e.g. in Marginalized Particle Filter (bdm::MPF). Alternatively, it can be used for automated connection to DS when the condition is observed
const RV &	_rvc () const
	access function
virtual void	condition (const vec &val)
	Substitute `val` for `rvc`.
RV	rvc
	Name of extension variable.
Logging of results
void	set_options (const string &opt)
	Set boolean options from a string.
void	log_add (logger *L, const string &name="")
	Add all logged variables to a logger.
void	logit (logger *L)
ivec	LIDs
	IDs of storages in loggers.
bool	opt_L_bounds
	Option for logging bounds.
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 &	posterior () const
const eprod *	_e () const
emix *	epredictor () const
	Constructs a predictive density $f(d_{t+1} \|d_{t}, \ldots d_{0})$ .
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) const
	Flatten the posterior as if to keep nu0 data.
Constructors
virtual BM *	_copy_ () const
Mathematical operations
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.
virtual mpdf *	predictor () const
	Constructs a conditional density 1-step ahead predictor.
Access to attributes
const RV &	_drv () const
void	set_drv (const RV &rv)
void	set_rv (const RV &rv)
double	_ll () const
void	set_evalll (bool evl0)
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	drv
	Random variable of the data (optional).
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.