Learning nonsingular phylogenies and hidden Markov models
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Learning mixtures of product distributions over discrete domains
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Distorted Metrics on Trees and Phylogenetic Forests
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
PAC-learnability of probabilistic deterministic finite state automata in terms of variation distance
Theoretical Computer Science
Fast and reliable reconstruction of phylogenetic trees with very short edges
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Separating populations with wide data: a spectral analysis
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
PAC-learnability of probabilistic deterministic finite state automata in terms of variation distance
ALT'05 Proceedings of the 16th international conference on Algorithmic Learning Theory
PAC learning axis-aligned mixtures of gaussians with no separation assumption
COLT'06 Proceedings of the 19th annual conference on Learning Theory
Approximating the best-fit tree under Lp norms
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Fast and reliable reconstruction of phylogenetic trees with indistinguishable edges
Random Structures & Algorithms
Learning mixtures of arbitrary distributions over large discrete domains
Proceedings of the 5th conference on Innovations in theoretical computer science
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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 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. [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.