Tsachy Weissman, Stanford University
Abstract:
A continuous-time finite-power process with distribution P is observed through an Additive White Gaussian Noise channel, at a given signal-to-noise ratio (SNR), and is estimated by an estimator that would have minimized the mean-square error if the process had distribution Q. We show that the causal filtering mean-square error (MSE) achieved at SNR level snr is equal to the average value of the noncausal (smoothing) MSE achieved with a channel whose SNR is chosen uniformly distributed between 0 and snr. Emerging as the bridge for equating these quantities are mutual information and relative entropy. Our results build on and extend those of [Duncan 1970], [Guo, Shamai and Verdu 2005], and [Verdu 2009] in ways that will be explained. Extensions that accommodate the presence of feedback - and implications on minimax estimation and mismatched decoding - will be briefly discussed.
Biography:
Tsachy Weissman received the B.Sc. and Ph.D. degrees, both in electrical engineering, from the Technion in 1997 and 2001, respectively. During 2002-2003 he was visiting the Statistics Department at Stanford, and was with the information theory research group at Hewlett-Packard Laboratories, to which he currently consults. Hw has been on the faculty of the Electrical Engineering department at Stanford since 2003, spending the two academic years 2007-2009 on leave at the Technion Department of Electrical Engineering. His research interests span information theory and its applications, and statistical signal processing. His papers thus far have focused mostly on data compression, communications, prediction, denoising, and learning. Hw is inventor of several patents in these areas and involved in a number of high-tech companies as a researcher or member of the technical board. Among his more recent awards are the Rothschild Foundation Scholarship, the NSF CAREER Grant, and a Horev fellowship. He is a co-recipient of the 2006 joint IT/COM societies best paper award.