EE Systems Seminar

This talk is one of a series of talks given by Professor Tarokh as part of the Moore Scholar program.

Abstract:  Two of the most profound results in Extreme Value Theory are the Theorem of Fisher-Tippett and Gnedenko,  and the Theorem of Pickands, Balkema and de Haan.  In spite of the fact that they are extremely powerful, they remain (in my opinion) highly  under-appreciated in engineering applications.

We will  review these theorems, and show some applications as described below:

a) Claude Shannon long ago has computed the ultimate limit of transmission (capacity) for certain channels.  However, the "ultimate throughput" of schedulers are not known. We will use the Theorem of Fisher-Tippett and Gnedenko, and derive the capacity of certain schedulers. This approach is valid even if the capacity of the single link channels cannot be explicitly calculated!

b) Using the same theorem, we will discuss the ultimate gain of multiuser antenna selection diversity schemes.

c) For a distributed random array (e.g. in radar or astronomy) scenario, we will calculate the asymptotic distributions of the beam side-lobes.

d) Most remarkably, inspired by Pickands, Balkema and de Haan's Theorem, we propose a method to predict "rare events" in data analysis with superb performance. We verify the performance of our method on both real and synthetic data.
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Bio:  Vahid Tarokh is Rhodes Family Professor of Electrical and Computer Engineering, Professor of Mathematics, and Computer Science at Duke University. He worked at AT&T Labs-Research until 2000, and subsequently at MIT (as an Associate Professor of EECS) until 2002. He joined Harvard University as Perkins Professor of Applied Mathematics and Hammond Vinton Hayes Senior Fellow of Electrical Engineering. He then joined Duke University in January 2018.

His current research focuses on statistical signal processing and applications. Dr. Tarokh has received a number of awards, and holds four honorary degrees.