The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 16, Number 2 (2006), 583-614.
Learning nonsingular phylogenies and hidden Markov models
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.
Ann. Appl. Probab., Volume 16, Number 2 (2006), 583-614.
First available in Project Euclid: 29 June 2006
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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