I am looking for a research paper that basically describes a hidden markov model that has multiple observations, and some observations that have conditional dependencies. For example, please consider the following figure that shows two latent states with 5 observed variables. Here the variable obs5 is dependent on it's parent obs1-obs4. I am aware of HMMs that have single level of observed variables. However, I am not able to find any literature that has the following graphical model structure. So my question is, are there any works/ research papers that model such HMMs? enter image description here


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I am looking for a research paper that basically describes a hidden markov model that has multiple observations,...

If there was no obs5, it would have been called a Dynamic Naive Bayes Model (DNB).There aren't many software packages/modules that can deal with DNB's, but since the observed variables are indepenedent, you can basically take an open source HMM module or code your own and expand its "Baum-Welch" method to calculate the likelihoods of multiple (independent) variables (as opposed to let's say, just obs1).

...and some observations that have conditional dependencies.

Now, that is black magic territory (!). The general name of the structure you posted is a Dynamic Bayesian Network. There aren't many mortals who have achieved to tame that beast.

Joke aside, it is a complicated field and the theoretical solutions that exist can only do so subject to various constraints and I do not know of many DBN packages that you can use out of the box. Especially trying to do structure learning or performing inference on DBN's requires a black-belt in graphical probabilistic models.

Kevin Murphy (who has that black belt) gave this presentation on HMMs, DBNs, etc. Maybe good for a quick overview.

  • $\begingroup$ thanks for the explanation. Yes, they are indeed dynamic bayesian network. In fact, they are also referred by dynamic template models [Daphne Koller PGM principles and techniques](again a very specific type of dynamic bayes-nets). However, as stated above my only concern is with those dependent observations. I don't require any software packages, I just want to know if there are research papers that target similar PGM structures. $\endgroup$
    – Rkz
    Commented Aug 21, 2014 at 13:53

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