Vidyasagar, Mathukumalli (Tata Consultancy Services)

A Realization Theory for Hidden Markov Models: The Partial Realization Problem

Scheduled for presentation during the Regular Session "Nonlinear Estimation and Identification" (ThP09), Thursday, July 27, 2006, 15:20−15:45, Room J

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on May 19, 2024

Abstract

Suppose $m$ is a natural number and let $M := { 1, ldots , m }$. Suppose ${ Y_t }$ is a stationary stochastic process assuming values in $M$. In this paper, we study the so-called `exact' partial realization problem for hidden Markov models (HMM's), which can be stated as follows: Given the frequencies of all $k$-tuples over $M$ for some fixed integer $k$, construct a HMM that {em exactly/} reproduces these frequencies. For the `exact' partial realization problem, a well-known solution is to model the process as a $(k-1)$-step Markov process. In this paper, it is shown that this well-known partial realization is {em the only possible/} partial realization satisfying certain natural conditions.