Communications of the ACM
Elements of information theory
Elements of information theory
On the learnability of discrete distributions
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Evaluation may be easier than generation (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Efficient learning of typical finite automata from random walks
Information and Computation
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
Learning mixtures of product distributions over discrete domains
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
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
Robust PCA and clustering in noisy mixtures
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Foundations and Trends® in Theoretical Computer Science
Separating populations with wide data: a spectral analysis
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Efficiently learning mixtures of two Gaussians
Proceedings of the forty-second ACM symposium on Theory of computing
Communications of the ACM
Learning mixtures of arbitrary distributions over large discrete domains
Proceedings of the 5th conference on Innovations in theoretical computer science
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We propose and analyze a new vantage point for the learning of mixtures of Gaussians: namely, the PAC-style model of learning probability distributions introduced by Kearns et al. [13]. Here the task is to construct a hypothesis mixture of Gaussians that is statistically indistinguishable from the actual mixture generating the data; specifically, the KL divergence should be at most ε. In this scenario, we give a poly(n/ε) time algorithm that learns the class of mixtures of any constant number of axis-aligned Gaussians in Rn. Our algorithm makes no assumptions about the separation between the means of the Gaussians, nor does it have any dependence on the minimum mixing weight. This is in contrast to learning results known in the “clustering” model, where such assumptions are unavoidable. Our algorithm relies on the method of moments, and a subalgorithm developed in [9] for a discrete mixture-learning problem.