Home | Quick Search | Advanced Search | Bibliography submission | Bibliography submission using bibtex | Bibliography submission using bibtex file | Links | Help | Internal


TitleViterbi sequences and polytopes
Author(s) Eric H. Kuo
TypeArticle in Journal
AbstractA Viterbi path of length n of a discrete Markov chain is a sequence of n + 1 states that has the greatest probability of occurring 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.
KeywordsMarkov chains, Viterbi paths, Polytopes
URL http://www.sciencedirect.com/science/article/pii/S074771710500115X
JournalJournal of Symbolic Computation
Pages151 - 163
NoteComputational Algebraic Statistics Computational Algebraic Statistics
Translation No
Refereed No