Learning nonsingular phylogenies and hidden Markov models

TL;DR

This paper introduces a polynomial-time algorithm for learning nonsingular phylogenies and hidden Markov models, emphasizing the importance of the nonsingularity condition for tractable learning, unlike the hard case without it.

Contribution

The paper establishes the significance of nonsingularity in learning phylogenies and HMMs and provides the first polynomial-time algorithm under this condition.

Findings

Polynomial-time algorithm for nonsingular models

Nonsingularity condition is crucial for efficient learning

Learning without nonsingularity is as hard as learning parity with noise

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.