The problem of reducing a Hidden Markov Model (HMM) to one smaller dimension that exactly reproduces the same marginals is tackled by using system-theoretic approach. Realization theory tools are extended HMMs leveraging suitable algebraic representations probability spaces. We propose two algorithms return coarse-grained equivalent obtained stochastic projection operators: first returns models...

It reviews the theory of Hidden Filter Hidden Markov Models and presents an extension, Mixed State Hidden Markov Models, developed jointly by Andrew Fraser and myself under his supervision. This manuscript version has only trivial differences from the original.

This article concerns the study of the asymptotic properties of the maximum likelihood estimator (MLE) for the general hidden semi-Markov model (HSMM) with backward recurrence time dependence. By transforming the general HSMM into a general hidden Markov model, we prove that under some regularity conditions, the MLE is strongly consistent and asymptotically normal. We also provide useful expres...

This paper describes Hidden Markov Model and its application in natural language process, first introduces the basic concept of Hidden Markov Model, then introduces the three basic issues and the basic algorithm to solve the problems, finally gives the demonstration of the application of Chinese part-of-speech tagging and speech recognition via Hidden Markov Model.

We introduce a new probability distribution over a potentially infinite number of binary Markov chains which we call the Markov Indian buffet process. This process extends the IBP to allow temporal dependencies in the hidden variables. We use this stochastic process to build a nonparametric extension of the factorial hidden Markov model. After constructing an inference scheme which combines sli...