Nonparametric Estimation via Convex Programming
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Date: 05-05-2009
Start Time:
1:00pm
End Time: 2:00pm
Speaker: Arkadi Nemirovski, School of Industrial and Systems Engineering: Georgia Institute of Technology
Location: Mudd 303
ABSTRACT
In the talk, based on joint research with Professor Anatoli Iouditski, University of Joseph Fourier, Grenoble, France, we consider the problem of estimating a linear form of a "signal" x known to belong to a given convex compact set via an observation of a random variable with distribution parameterized by the signal. We show that under certain structural assumptions on the distribution, a nearly optimal in the minimax sense estimate possesses a simple structure and can be built efficiently via Convex Programming. The assumptions in question are satisfied in the following cases:
(a) finitely supported distribution affinely parameterized by x; (b) Gaussian distribution with fixed covariance and the mean affinely parameterized by x; (c) Poisson distribution with the natural parameter affinely parameterized by x; (e) "direct product" of the above: the observation is comprised of independent realizations of random variables with distributions of the types (a) -- (c). Finally, we indicate some potential applications of the proposed estimator.
BIO
Dr. Arkadi Nemirovski got his Ph.D. (Math, 1974) from Faculty of Mechanics and Mathematics, Moscow State University. Till 1993, he held various research positions in Moscow; in 1993-2005, he was a professor at the Technion, Israel. Since 2005, he is Jh. Hunter Jr. Academic Chair and professor at ISyE, GaTech. His major areas of research are efficient algorithms and complexity in Convex Optimization, Robust Optimization, and non-parametric statistics; on these subjects, he (co-)authored 5 research monographs and over 110 journal papers. Dr. Nemirovski was awarded the Fulkerson Prize of MPS and AMS (1982, with L. Khachiyan and D. Yudin), the Dantzig Prize of MPS and SIAM (1991, with M. Grotschel) and the John von Neumann Theory Prize of INFORMS (2003, with M. Todd).