CODEWITHSUNDEEP
rmachine-learninghidden-markov-models
Alessandro Grassi
Alessandro Grassi

Reputation: 165

Hmm training with multiple observations and mhsmm package in R

i wanted to train a new hmm model, by means of Poisson observations that are the only thing i know. I'm using the mhsmm package for R.

The first thing that bugs me is the initialization of the model, in the examples is:

J<-3
initial <- rep(1/J,J)
P <- matrix(1/J, nrow = J, ncol = J)
b <- list(lambda=c(1,3,6))
model = hmmspec(init=initial, trans=P, parms.emission=b,dens.emission=dpois.hsmm)

in my case i don't have initial values for the emission distribution parameters, that's what i want to estimate. How?

Secondly: if i only have observations, how do i pass them to 

h1 = hmmfit(list_of_observations, model ,mstep=mstep.pois)

in order to obtain the trained model? list_of_observations, in the examples, contains a vector of states, one of observations and one of observation sequence length and is usually obtained by a simulation of the model:

list_of_observations = simulate(model, N, rand.emis = rpois.hsmm)

EDIT: Found this old question with an answer that partially solved my problem: MHSMM package in R-Input Format? These two lines did the trick:

train <- list(x = data.df$sequences, N = N)
class(train) <- "hsmm.data"

where data.df$sequences is the array containing all observations sequences and N is the array containing the count of observations for each sequence. Still, the initial model is totally random, but i guess this is the way it is meant to be since it will be re-estimated, am i right?

Upvotes: 1

Views: 1417

Answers (2)

PaRb
PaRb

Reputation: 31

  • Goal: find estimates of the emission distribution but it also works for initial probability and transition matrix
  • Algorithm: needs initial estimate to start the optimisation from
  • You: have to provide an initial "guess" of the parameters

This may seem confusing at first, but the EM algorithm needs a point to start the optimisation. Then it makes some computations and it gives you a better estimate of your own initial guess (re-estimation, as you said). It is not able to just find the best parameters on its own, without being initialised.

From my experience, there is no general way to initialise the parameters that guarantee to converge to a global optimum, but it will depend more on the case at hand. That's why initialisation plays a critical role (mostly for emission distribution).

What I used to do in such a case is to separate the training data in different groups (e.g. percentiles of a certain parameter in the set), estimate the parameters on these groups, and then use them as initial parameter estimates for the EM algorithm. Basically, you have to try different methods and see which one works best.

I'd recommend to search the literature if similar problems have been solved with HMM, and try their initialisation method.

Upvotes: 0

lordbitin
lordbitin

Reputation: 195

The problem of initialization is critical not only for HMMs and HSMMs, but for all learning methods based on a form of the Expectation-Maximization algorithm. EM converges to a local optimum in terms of likelihood between model and data, but that does not always guarantee to reach the global optimum.

Upvotes: 0

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