Elements of information theory
Elements of information theory
On the Computational Complexity of Approximating Distributions by Probabilistic Automata
Machine Learning - Computational learning theory
Metrics and Similarity Measures for Hidden Markov Models
Proceedings of the Seventh International Conference on Intelligent Systems for Molecular Biology
Two Methods for Improving Performance of a HMM and their Application for Gene Finding
Proceedings of the 5th International Conference on Intelligent Systems for Molecular Biology
A Hidden Markov Model for Predicting Transmembrane Helices in Protein Sequences
ISMB '98 Proceedings of the 6th International Conference on Intelligent Systems for Molecular Biology
Clique Is Hard to Approximate within n1-o(1)
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
An Approximate L1-Difference Algorithm for Massive Data Streams
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Testing that distributions are close
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
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The basic theory of hidden Markov models was developed and applied to problems in speech recognition in the late 1960's, and has since then been applied to numerous problems, e.g. biological sequence analysis. In this paper we consider the problem of computing the most likely string generated by a given model, and its implications on the complexity of comparing hidden Markov models. We show that computing the most likely string, and approximating its probability within any constant factor, is NP-hard, and establish the NP-hardness of comparing two hidden Markov models under the L∞- and L1-norms. We discuss the applicability of the technique used to other measures of distance between probability distributions. In particular we show that it cannot be used to prove NP-hardness of determining the Kullback-Leibler distance between the probability distributions of two hidden Markov models, or of comparing them under the Lk-norm for any fixed even integer k.