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2007 JMLR JMLR 2007

A Probabilistic Analysis of EM for Mixtures of Separated, Spherical Gaussians

Abstract

We show that, given data from a mixture of k well-separated spherical Gaussians in ℜd, a simple two-round variant of EM will, with high probability, learn the parameters of the Gaussians to near-optimal precision, if the dimension is high (d >> ln k). We relate this to previous theoretical and empirical work on the EM algorithm. [abs] [ pdf ][ bib ] © JMLR 2007. (edit, beta)

🧭 Keyword Pioneer — gaussian mixture
🐝 Cross-Pollinator — Artificial Intelligence, Computer Science, Computer Vision, Data Science & Analytics, Deep Learning, Healthcare & Medicine, Interdisciplinary, Knowledge & Reasoning, Machine Learning, Mathematics & Optimization, Natural Language Processing, Reinforcement Learning, Robotics, Speech & Audio
🐣 Hot Topic Early Bird — expectation maximization

Authors

Sanjoy Dasgupta , Leonard Schulman

Topics

Machine Learning > Core Methods > Clustering Machine Learning > Optimization & Theory > Statistical Learning Machine Learning > Bayesian & Probabilistic > Probabilistic Modeling Machine Learning > Bayesian & Probabilistic > Bayesian Inference

Keywords

parameter estimation expectation maximization high-dimensional learning mixture model gaussian mixture probabilistic analysis spherical gaussian
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