Upcoming Webinar: CAMSAP 2017 Plenary - 13 December 2017, Dr. Nikos Sidiropoulos

CAMSAP 2017 Plenary - Tensors and Probability: An Intriguing Union

Abstract: We reveal an interesting link between tensors and multivariate statistics. The rank of a multivariate probability tensor can be interpreted as a nonlinear measure of statistical dependence of the associated random variables. Rank equals one when the random variables are independent, and complete statistical dependence corresponds to full rank; but we show that rank as low as two can already model strong statistical dependence. In practice, we usually work with random variables that are neither independent nor fully dependent—partial dependence is typical, and can be modeled using a low-rank multivariate probability tensor. Directly estimating such a tensor from sample averages is impossible even for as few as ten random variables taking ten values each—yielding a billion unknowns; but we often have enough data to estimate lower-order marginalized distributions. We prove that it is possible to identify the higher-order joint probabilities from lower order ones, provided that the higher-order probability tensor has low-enough rank, i.e., the random variables are only partially dependent. We also provide a computational identification algorithm that is shown to work well on both simulated and real data. The insights and results have numerous applications in estimation, hypothesis testing, completion, machine learning, and system identification. Low-rank tensor modeling thus provides a “universal” non-parametric (model-free) alternative to probabilistic graphical models. 

Biography

Nikos Sidiropoulos received the Diploma in Electrical Engineering from the Aristotelian University of Thessaloniki, Greece, and the M.S. and Ph.D. degrees in Electrical Engineering from the University of Maryland–College Park, in 1988, 1990, and 1992, respectively. 

He served as Assistant Professor at the University of Virginia (1997–1999); Associate Professor at the University of Minnesota–Minneapolis (2000–2002); Professor at the Technical University of Crete, Chania–Crete, Greece (2002–2011); and since 2011, he has been Professor at the University of Minnesota–Minneapolis, where he has been holding an ADC Chair in Digital Technology since 2015. His research interests are in signal processing, communications, optimization, tensor decomposition, and factor analysis. His current research focuses primarily on signal and tensor analytics and optimization-based algorithms, with applications in machine learning and communications.

Dr. Sidiropoulos received the NSF/CAREER award in 1998, and the IEEE Signal Processing Society (SPS) Best Paper Award in 2001, 2007, and 2011. He served as IEEE SPS Distinguished Lecturer (2008–2009), and as Chair of the IEEE Signal Processing for Communications and Networking Technical Committee (2007–2008), and was recently elected Vice President - Membership of the IEEE Signal Processing Society. He received the 2010 IEEE Signal Processing Society Meritorious Service Award, and the 2013 Distinguished Alumni Award from the University of Maryland, Department of Electrical and Computer Engineering. He is a Fellow of IEEE (2009) and a Fellow of EURASIP (2014).