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Evolutionary trees can be learned in polynomial time in the two-state general Markov model

By Mary Cryan, Leslie Ann Goldberg and Paul W. Goldberg

Abstract

The j-state general Markov model of evolution ( due to Steel) is a stochastic model concerned with the evolution of strings over an alphabet of size j. In particular, the two-state general Markov model of evolution generalizes the well-known Cavender-Farris-Neyman model of evolution by removing the symmetry restriction (which requires that the probability that a "0" turns into a "1" along an edge is the same as the probability that a "1" turns into a "0" along the edge). Farach and Kannan showed how to probably approximately correct ( PAC)-learn Markov evolutionary trees in the Cavender-Farris-Neyman model provided that the target tree satis es the additional restriction that all pairs of leaves have a sufficiently high probability of being the same. We show how to remove both restrictions and thereby obtain the rst polynomial-time PAC-learning algorithm ( in the sense of Kearns et al. [ Proceedings of the 26th Annual ACM Symposium on the Theory of Computing, 1994, pp. 273-282]) for the general class of two-state Markov evolutionary trees

Topics: QA76, QA
Publisher: Society for Industrial and Applied Mathematics
Year: 2001
DOI identifier: 10.1137/s0097539798342496
OAI identifier: oai:wrap.warwick.ac.uk:11659
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