The Annals of Applied Probability

Learning nonsingular phylogenies and hidden Markov models

Elchanan Mossel and Sébastien Roch

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Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 16, Number 2 (2006), 583-614.

Dates
First available in Project Euclid: 29 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1151592244

Digital Object Identifier
doi:10.1214/105051606000000024

Mathematical Reviews number (MathSciNet)
MR2244426

Zentralblatt MATH identifier
1137.60034

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40] 68T05: Learning and adaptive systems [See also 68Q32, 91E40] 92B10: Taxonomy, cladistics, statistics

Keywords
Hidden Markov models evolutionary trees phylogenetic reconstruction PAC learning

Citation

Mossel, Elchanan; Roch, Sébastien. Learning nonsingular phylogenies and hidden Markov models. Ann. Appl. Probab. 16 (2006), no. 2, 583--614. doi:10.1214/105051606000000024. https://projecteuclid.org/euclid.aoap/1151592244


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