Learning nonsingular phylogenies and hidden Markov models

In this paper, we study the problem of learning phylogenies and hidden Markov models. We call the Markov model nonsingular if all transtion 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. On the other hand, we give a polynomial-time algorithm for learning nonsingular phylogenies and hidden Markov models.

• Type: Conference
• Year: 2005
• Where: STOC
• Authors: Elchanan Mossel, Sébastien Roch
• Keywords: Algorithms, Markov Models, Nonsingularity Condition, STOC 2005, Transtion Matrices