New Analytical Tools to address Challenges in Data Science and Information Theory

Abstract: In the first part of my talk, I consider the following problem arising in data privacy. How do we extract accurate statistical information from modern-day databases while preserving privacy of individuals whose data is stored in the database? We propose an architecture that permits unrestrained querying of databases while providing provable guarantees on privacy. The performance of this architecture is governed by a utility-privacy trade-off. Leveraging tools from discrete geometry and analytic methods, I present a precise characterization of this trade-off in terms of the Ehrhart series of a suitably defined convex polytope. In the second part, we consider classical problems in multi-terminal information theory. We present two approaches that have yielded new results. The first approach is built on new ensembles of algebraic codes. The second approach is based on a connection between the findings of Shannon (1948) and Witsenhausen (1975, SIAM Disc. Math.). We present new coding strategies and characterize new inner bounds to the capacity region of fundamental network scenarios. Both approaches have yielded new results for classical problems that had resisted progress for over three decades.

Bio: Arun holds a Masters in Electrical Commn Engg from the Indian Institute of Science, a Masters in Mathematics from the Univ. of Michigan (UMICH) and a PhD in EECS from UMICH. Following his PhD, Arun worked for a year as a Research Scientist at Ericsson Research in San Jose, USA. In 2015, Arun joined the NSF Center for Science of Information as a Center-wide postdoctoral research fellow and worked under the advise of Prof. P R Kumar and Prof. Wojciech Szpankowski. Since 2018, he has been an Assistant Professor at the University of Tennessee at Knoxville. Arun's research interests are in Data Science, Information theory and Quantum Information Science.