Complexity of Comparing Hidden Markov Models
نویسندگان
چکیده
1 Baskin Center for Computer S ien e and Engineering, University of California, Santa Cruz, CA 95064, U.S.A. E-mail: rlyngsoe se.u s .edu 2 BiRC⋆ ⋆ ⋆, Department of Computer S ien e, University of Aarhus, Ny Munkegade, DK-8000 Århus C, Denmark. E-mail: storm daimi.au.dk. Abstra t The basi theory of hidden Markov models was developed and applied to problems in spee h re ognition in the late 1960's, and has sin e then been applied to numerous problems, e.g. biologi al sequen e analysis. In this paper we onsider the problem of omputing the most likely string generated by a given model, and its impli ations on the omplexity of omparing hidden Markov models. We show that omputing the most likely string, and approximating its probability within any onstant fa tor, is NP-hard, and establish the NP-hardness of omparing two hidden Markov models under the L∞and L1-norms. We dis uss the appli ability of the te hnique used to other measures of distan e between probability distributions. In parti ular we show that it annot be used to prove NP-hardness of determining the Kullba k-Leibler distan e between the probability distributions of two hidden Markov models, or of omparing them under the Lk-norm for any xed even integer k.
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