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

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Cryan, Mary, Goldberg, Leslie Ann and Goldberg, Paul W. (1998) Evolutionary trees can be learned in polynomial time in the two-state general Markov model. University of Warwick. Department of Computer Science. (Department of Computer Science research report). (Unpublished)

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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 generalises 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 PAC-learn Markov Evolutionary Trees in the Cavender-Farris-Neyman model provided that the target tree satisfies 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 first polynomial-time PAC-learning algorithm (in the sense of Kearns et al.) for the general class of Two-State Markov Evolutionary Trees.

Item Type: Report
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Computer Science
Library of Congress Subject Headings (LCSH): Markov processes, Graph theory
Series Name: Department of Computer Science research report
Publisher: University of Warwick. Department of Computer Science
Official Date: 20 July 1998
Dates:
DateEvent
20 July 1998Completion
Number: Number 347
Number of Pages: 21
DOI: CS-RR-347
Institution: University of Warwick
Theses Department: Department of Computer Science
Status: Not Peer Reviewed
Publication Status: Unpublished
Funder: European Strategic Programme of Research and Development in Information Technology (ESPRIT), Engineering and Physical Sciences Research Council (EPSRC)
Grant number: 20244 (ESPRIT), 21726 (ESPRIT), GR/L60982 (EPSRC)
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