Date of this Version
The Annals of Applied Probability
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.
hidden Markov models, evolutionary trees, phylogenetic reconstruction, PAC learning
Mossel, E., & Roch, S. (2006). Learning Nonsingular Phylogenies and Hidden Markov Models. The Annals of Applied Probability, 16 (2), 583-614. http://dx.doi.org/10.1214/105051606000000024
Date Posted: 27 November 2017
This document has been peer reviewed.