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Empirical Processes, Typical Sequences and Coordinated Actions
Abstract: Recent work by Cuff, Permuter and Cover on coordination via communication has revealed a fascinating aspect of strongly typical sequences --- they can be thought of as a means of reproducing relative frequencies of symbols emitted by stationary memoryless sources using finite communication resources. This viewpoint has a number of useful and far-reaching implications in such settings as distributed control and decision-making, network security, and statistical learning. However, strong typicality, as it pertains to approximating source distributions by relative frequencies in the sense of total variation, is not appropriate for continuous alphabet sources. In this talk, I will present a generalization of typicality that works for a wide class of abstract alphabets (so-called standard Borel spaces, which include all conceivable alphabets of practical interest). This new notion makes fundamental use of an object known in modern mathematical statistics as the empirical process, which is used to characterize the fluctuations of sample averages of functions in a given class around their true expectations. The proposed new notion of typicality possesses a minimal set of properties that make it useful in the context of abstract alphabets. To show this, I will use it to derive single-letter expressions for the minimal achievable rates in two source coding scenarios that can be viewed as generation of coordinated actions in a two-node network. One feature of note is that the achievability proofs are as transparent as in the finite-alphabet case.
Biography: Maxim Raginsky received the B.S. and M.S. degrees in 2000 and the Ph.D. degree in 2002 from Northwestern University, all in electrical engineering. He has held research positions with Northwestern, the University of Illinois at Urbana-Champaign (where he was a Beckman Foundation Fellow from 2004 to 2007), and Duke University. In 2012, he has returned to the UIUC, where he is currently an Assistant Professor with the Department of Electrical and Computer Engineering and the Coordinated Science Laboratory. His research interests lie at the intersection of information theory, learning, and control.