Markov Observation Models
This work addresses a theoretical limitation in modeling sequential data for researchers in statistics and machine learning, representing an incremental extension of existing models.
The authors tackled the problem of extending Hidden Markov Models to allow observations that themselves follow a Markov chain, developing an Expectation-Maximization algorithm and a dynamic programming method for estimation and tracking.
Herein, the Hidden Markov Model is expanded to allow for Markov chain observations. In particular, the observations are assumed to be a Markov chain whose one step transition probabilities depend upon the hidden Markov chain. An Expectation-Maximization analog to the Baum-Welch algorithm is developed for this more general model to estimate the transition probabilities for both the hidden state and for the observations as well as to estimate the probabilities for the initial joint hidden-state-observation distribution. A believe state or filter recursion to track the hidden state then arises from the calculations of this Expectation-Maximization algorithm. A dynamic programming analog to the Viterbi algorithm is also developed to estimate the most likely sequence of hidden states given the sequence of observations.