HFMfit: Fit a HFM Model

In treeHFM: Hidden Factor Graph Models

Description

The functions fits an HFM (Hidden Factor Graph Model) to the (tree structured) data.

Usage

	HFMfit(data,nHStates,dataNodeIndices,priorInit,transmatInit,transInitDiv,
	type,emissionProb=c(),SigmaInit=c(), muInit=c() )

Arguments

data	The observations. A list of measurements for every observation. An entry can be a matrix of size KxN, whereas K is the dimension of the data and N the lenght of the sequence or of size 1xK whereas the entries are discrete.
nHStates	Number of hidden states H
dataNodeIndices	The data structure. A list of the toplogy of every data entry of the format [parentIndex childIndex].
priorInit	The inital state probabilities
transmatInit	The initial transtition probabilities for sequential transitions (H x H)
transInitDiv	The initial transtition probabilities for splitting events (H x (H*H)
type	Type of the data. ('d' discrete or 'c' continous)
emissionProb	Initial emission probilities for discrete data, a matrix of size E x H, whereas E are the number of discrete observable states.
SigmaInit	Initial covariance matrix for continous data
muInit	Initial means for continous data

Details

The algorithm fits an HFM to sequential data (in this case essentially a Hidden Markov Model is fitted) or to data that is structured as a binary tree. An HFM consists of two transition probability matrices. One for the sequential transitions and one for transitions where a splitting happens.

Value

An HFM:

$initProb	The initial probabilities (prior).
$transMatSeq	The transition matrix for sequential events
$transMatDiv	The transition matrix for division events
$ll	The log likelihood
$emission	The emission probabilities of the hidden states

Author(s)

Henrik Failmezger, [e-mail]

Examples

## Fit a discrete treeHFM ## 
nOStates = 3;
nHStates = 2;
#
T = 1;
nex = 10;
obs1=sample(1:nOStates,5,replace=T)
obs2=sample(1:nOStates,5,replace=T)
data=list()
data[[1]]=obs1;
#
nodeIndices1=cbind(c(0,1,2,2,4),c(1,2,3,4,5));
dataNodeIndices=list()
dataNodeIndices[[1]]=nodeIndices1;
prior1=array(1,nHStates);
priorInit = array(1,nHStates)/nHStates;
transmatInit = matrix(1,nHStates,nHStates)*(1/nHStates);
transInitDiv= matrix(1,nHStates,nHStates*nHStates)*(1/(nHStates*nHStates))
obsmatInit = matrix(sample(1:nOStates,nHStates*nOStates,replace=T),nHStates,nOStates);
obsmatInit=obsmatInit/rowSums(obsmatInit,1);
hfm=HFMfit(data,nHStates,dataNodeIndices,priorInit,transmatInit,transInitDiv,
'd',emissionProb=obsmatInit);
## Fit a continous treeHFM ## 
nHStates = 2;
########create observation sequences########
obs1 <- rbind(runif(10,0,1),runif(10,0,1))
obs2 <- rbind(runif(8,0,1),runif(8,0,1))
data=list()
data[[1]]=obs1
data[[2]]=obs2
######### create guesses for gaussian covariance matrix and means #########
mc2 <- Mclust(t(cbind(obs1,obs2)), G=2)
muInit=mc2$parameters$mean;
SigmaInit=mc2$parameters$variance$sigma
#########create tree topology####################################
nodeIndices1=cbind(c(0,1,2,3,3,4,5,6,7,8),c(1,2,3,4,5,6,7,8,9,10));
nodeIndices2=cbind(c(0,1,2,3,4,4,5,6),c(1,2,3,4,5,6,7,8));
dataNodeIndices=list()
dataNodeIndices[[1]]=nodeIndices1;
dataNodeIndices[[2]]=nodeIndices2;
######### create guesses for prior and transition matrices#########
prior1=array(1,nHStates);
priorInit = array(1,nHStates)/nHStates;
transmatInit = matrix(1,nHStates,nHStates)*(1/nHStates);
transInitDiv= matrix(1,nHStates,nHStates*nHStates)*(1/(nHStates*nHStates))
#
hfm=HFMfit(data,nHStates,dataNodeIndices,priorInit,transmatInit,transInitDiv,'c',
SigmaInit=SigmaInit, muInit=muInit);
#

treeHFM documentation built on May 30, 2017, 3:01 a.m.