Monday October 18 4:00 - 5:00 PM Kelley 1001
Misha Belkin Associate Professor Department of Computer Science and Statistics Ohio State University Learning Mixtures of Gaussians The study of Gaussian mixture distributions goes back to the late 19th century, when Pearson introduced the method of moments to analyze the statistics of a crab population. They have since become one of the most popular tools of modeling and data analysis, extensively used in speech recognition and other fields. Yet their properties are still not well understood. Widely used algorithms, such as Expectation Maximization (EM) often fail even on simple generated data and their theoretical properties are often unclear. In my talk I will discuss some theoretical aspects of the problem of learning Gaussian mixtures. In particular, I will discuss our recent result, which, in a certain sense, completes work on an active recent topic in theoretical computer science by establishing quite general conditions for polynomial learnability of mixtures by using techniques based on techniques of semi-algebraic geometry. If time permits, I will also discuss a set of practical algorithms base! d on spectral methods, which can potentially overcome some of the shortcomings of Expectation Maximization. The talk is based on joint work with Kaushik Sinha, Tao Shi and Bin Yu. Biography Mikhail Belkin is an Assistant Professor in Computer Science and Statistics departments at the Ohio State University. He received his PhD from the Mathematics department at the University of Chicago in 2003. His research focuses on designing and analyzing algorithms for statistical machine learning based on non-linear structure of high dimensional data, and, in particular, on manifold and spectral methods, as well as their applications. He is also interested in connections between machine learning and human cognition. Mikhail Belkin was a co-organizer of the Chicago Machine Learning Summer School in 2005, the Workshop on Geometry, Random Matrices, and Statistical Inference in SAMSI in 2007, and the 2009 Machine Learning Summer School/Workshop on Theory and Practice of Computational Learning. He received the National Science Foundation Career Award in 2006. His research is currently supported by the National Science Foundation and the U.S Air Force Research Foundation. _______________________________________________ Colloquium mailing list [email protected] https://secure.engr.oregonstate.edu/mailman/listinfo/colloquium
