## On Two Problems in Coded Statistical InferenceNir Weinberger ## AbstractWhile statistical inference and information theory are deeply related fields, problems which lie at the intersection of both disciplines usually fall between the two stools, and lack definitive answers. In this talk, I will discuss recent advances in two such problems. In the first part of the talk, I will discuss a distributed hypothesis testing problem, in which the hypotheses regard the joint statistics of two sequences, one available to the decision function directly (as side information), while the other is conveyed through a limited-rate link. The goal is to design a system which obtains the optimal trade-off between the false-alarm and misdetection exponents. I will define a notion of "channel detection codes", and show that the optimal exponents of the distributed hypothesis testing problem is directly related to the exponents of these codes. Then, I will discuss a few bounds on the exponents of channel detection codes, as well as prospective improvements. This approach has a two merits over previous works: It is suitable for any pair of memoryless joint distributions, and it provides bounds on the entire false-alarm/misdetection curve, rather than just bounds on its boundary points (Stein's exponent). In the second part of the talk (time permitting), I will discuss a parameter estimation problem over an additive Gaussian noise channel with bandlimited input. In case one is allowed to design both the modulator and the estimator, the absolute \$alpha$-th moment of the estimation error can decrease exponentially with the transmission time. I will discuss several new upper (converse) bounds for the optimal decrease rate. Joint work with Yuval Kochman (Hebrew university) and Neri Merhav (Technion). ## BioNir Weinberger is a post-doctoral fellow at Tel Aviv University. He has received the B.Sc. and M.Sc. degrees (both summa cum laude) from Tel-Aviv University in 2006 and 2009, respectively, and completed his Ph.D. studies at the Technion, Israel Institute of Technology in 2016. He has served as an algorithm Engineer in the Israeli Defense Forces, working in Communications and Signal Processing, from 2006 to 2013. He has been granted several scholarships for his Ph.D. studies, and his ISIT 2016 paper entitled "A Large Deviations Approach to Secure Lossy Compression" and co-authored with Prof. Neri Merhav, was one of 6 finalists for the best student paper award. |