# bdm::MixEF Class Reference

Mixture of Exponential Family Densities. More...

## 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:

where is a known function of past outputs, are component weights, and component parameters are assumed to be mutually independent. is an aggregation af all component parameters and weights, i.e. .

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.

`#include <mixtures.h>`

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 & | posterior () const
emix * | epredictor () const
| Constructs a predictive density .
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).
virtual void | flatten (const BMEF *B)
| Flatten the posterior according to the given BMEF (of the same type!).
BMEF * | _copy_ () const
void | from_setting (const Setting &set)
| This method arrange instance properties according the data stored in the Setting structure.
virtual string | to_string ()
| This method returns a basic info about the current instance.
virtual void | to_setting (Setting &set) const
| This method save all the instance properties into the Setting structure.
virtual void | validate ()
| This method TODO.
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 conditional density of 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 .
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.
## 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
virtual void | set_options (const string &opt)
| Set boolean options from a string, recognized are: "logbounds,logll".
virtual void | log_add (logger &L, const string &name="")
| Add all logged variables to a logger.
virtual void | logit (logger &L)
ivec | LIDs
| IDs of storages in loggers 4:[1=mean,2=lb,3=ub,4=ll].
ivec | LFlags
| Flags for logging - same size as LIDs, each entry correspond to the same in LIDs.

## Member Function Documentation

BMEF* bdm::BMEF::_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 from bdm::BM.

Reimplemented in bdm::ARX.

References bdm_error.

Referenced by init().

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_mix::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::eDirich::mean(), bdm::multiBM::posterior(), and weights.

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

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

- mixtures.h
- mixtures.cpp