Mathematics – Combinatorics
Scientific paper
2004-01-24
Journal of Symbolic Computation 41 (2006) 151-163
Mathematics
Combinatorics
15 pages, 2 figures, to appear in Journal of Symbolic Computation
Scientific paper
10.1016/j.jsc.2005.04.007
A Viterbi path of length n of a discrete Markov chain is a sequence of n+1 states that has the greatest probability of ocurring in the Markov chain. We divide the space of all Markov chains into Viterbi regions in which two Markov chains are in the same region if they have the same set of Viterbi paths. The Viterbi paths of regions of positive measure are called Viterbi sequences. Our main results are (1) each Viterbi sequence can be divided into a prefix, periodic interior, and suffix, and (2) as n increases to infinity (and the number of states remains fixed), the number of Viterbi regions remains bounded. The Viterbi regions correspond to the vertices of a Newton polytope of a polynomial whose terms are the probabilities of sequences of length n. We characterize Viterbi sequences and polytopes for two- and three-state Markov chains.
No associations
LandOfFree
Viterbi Sequences and Polytopes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Viterbi Sequences and Polytopes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Viterbi Sequences and Polytopes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-420138