Department of Electrical Engineering Seminar Series Speaker: Prof. Ayfer Ozgur Aydin Stanford University Title: A Geometric Approach to two Problems in Networks: Learning High-Dimensional Distributions and Communication with Relays Date: Thursday, October 18, 2018 Time: 4:30 pm Room: Engineering Quadrangle B205 Host: Prof. Yuxin Chen Abstract: We investigate the pivotal role geometry can play in characterizing the fundamental limits of information flow in two different network problems. We first consider a classical problem in network information theory: characterizing the capacity of a so-called relay channel. Even though the relay channel has been one of the central problems in network information theory, its capacity remains unknown for almost four decades. We solve an open problem posed by Cover in 1987. This problem, which Cover calls the "Capacity of the Relay Channel", corresponds to characterizing the capacity of this channel at one special operating point. Our approach is geometric and builds on an extension we develop for the isoperimetric inequality on a high-dimensional sphere. We then turn to another network problem, where the end goal is not to communicate a message but learn a high-dimensional distribution or parameter from its distributed samples under communication constraints. We first provide a geometric characterization of Fisher information from quantized samples. We then use this characterization to prove tight minimax bounds for distributed estimation of common statistical models (such as the product Bernoulli model, multinomial model, dense/sparse Gaussian location models). Our results show that the impact of the communication constraint can be drastically different depending on the tail behavior of the score function of the model. Some of our results recover or strengthen existing results in this area with simpler and more transparent proofs. We conclude with a discussion on future directions in the intersection of geometry and information theory. First part of the talk is joint work with Xiugang Wu and Leighton Barnes. Second part is joint work with Leighton Barnes, Yanjun Han and Tsachy Weissman. Bio: Ayfer Ozgur received her Ph.D. degree in 2009 from the Information Processing Group at EPFL, Switzerland. In 2010 and 2011, she was a post-doctoral scholar at the same institution. She is an Assistant Professor in the Electrical Engineering Department at Stanford University since 2012. Her research interests include distributed communication and learning, wireless systems, and information theory. Dr. Ozgur received the EPFL Best Ph.D. Thesis Award in 2010, an NSF CAREER award in 2013, the Okawa Foundation Research Grant and the IEEE 2018 Communication Theory Technical Committee (CTTC) Early Achievement Award in 2018. This seminar is supported with funds from the Korhammer Lecture Series.