On the learnability of discrete distributions
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Estimating a mixture of two product distributions
COLT '99 Proceedings of the twelfth annual conference on Computational learning theory
Learning mixtures of arbitrary gaussians
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Evolutionary Trees Can be Learned in Polynomial Time in the Two-State General Markov Model
SIAM Journal on Computing
A Spectral Algorithm for Learning Mixtures of Distributions
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
A Two-Round Variant of EM for Gaussian Mixtures
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
Learning Mixtures of Gaussians
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Spectral Partitioning of Random Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Learning nonsingular phylogenies and hidden Markov models
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Spectral norm of random matrices
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On Learning Mixtures of Heavy-Tailed Distributions
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Learning mixtures of product distributions over discrete domains
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Routing, disjoint paths, and classification
Routing, disjoint paths, and classification
A rigorous analysis of population stratification with limited data
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
PAC learning axis-aligned mixtures of gaussians with no separation assumption
COLT'06 Proceedings of the 19th annual conference on Learning Theory
An adaptive spectral heuristic for partitioning random graphs
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
The spectral method for general mixture models
COLT'05 Proceedings of the 18th annual conference on Learning Theory
On spectral learning of mixtures of distributions
COLT'05 Proceedings of the 18th annual conference on Learning Theory
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In this paper, we consider the problem of partitioning a small data sample drawn from a mixture of k product distributions. We are interested in the case that individual features are of low average quality γ, and we want to use as few of them as possible to correctly partition the sample. We analyze a spectral technique that is able to approximately optimize the total data size--the product of number of data points n and the number of features K--needed to correctly perform this partitioning as a function of 1/γ for K n. Our goal is motivated by an application in clustering individuals according to their population of origin using markers, when the divergence between any two of the populations is small.