Statistics Papers

Document Type

Journal Article

Date of this Version

2006

Publication Source

The Annals of Applied Probability

Volume

16

Issue

2

Start Page

583

Last Page

614

DOI

10.1214/105051606000000024

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.

Keywords

hidden Markov models, evolutionary trees, phylogenetic reconstruction, PAC learning

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Date Posted: 27 November 2017

This document has been peer reviewed.