Open Access
May 2006 Learning nonsingular phylogenies and hidden Markov models
Elchanan Mossel, Sébastien Roch
Ann. Appl. Probab. 16(2): 583-614 (May 2006). DOI: 10.1214/105051606000000024


In this paper we study the problem of learning phylogenies and hidden Markov models. We call a Markov model nonsingular if all transition matrices have determinants bounded away from 0 (and 1). We highlight the role of the nonsingularity condition for the learning problem. Learning hidden Markov models without the nonsingularity condition is at least as hard as learning parity with noise, a well-known learning problem conjectured to be computationally hard. On the other hand, we give a polynomial-time algorithm for learning nonsingular phylogenies and hidden Markov models.


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Elchanan Mossel. Sébastien Roch. "Learning nonsingular phylogenies and hidden Markov models." Ann. Appl. Probab. 16 (2) 583 - 614, May 2006.


Published: May 2006
First available in Project Euclid: 29 June 2006

zbMATH: 1137.60034
MathSciNet: MR2244426
Digital Object Identifier: 10.1214/105051606000000024

Primary: 60J10 , 60J20 , 68T05 , 92B10

Keywords: evolutionary trees , Hidden Markov models , PAC learning , phylogenetic reconstruction

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.16 • No. 2 • May 2006
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