Bodhi Sen is a Professor of Statistics at Columbia University, New York. He completed his Ph.D in Statistics from University of Michigan, Ann Arbor, in 2008. Prior to that, he was a student at the Indian
Statistical Institute, Kolkata, where he received his Bachelors (2002) and Masters (2004) in Statistics. His core statistical research centers around nonparametrics --- function estimation (with special
emphasis on shape constrained estimation), theory of optimal transport and its applications to statistics, empirical Bayes procedures, kernel methods, likelihood and bootstrap based inference, etc. He is also actively involved in interdisciplinary research, especially in astronomy.
His honors include the NSF CAREER award (2012), and the Young Statistical Scientist Award (YSSA) in the Theory and Methods category from the International Indian Statistical Association (IISA). He is an elected fellow of the Institute of Mathematical Statistics (IMS).
Talk: Multivariate Distribution-free testing using Optimal Transport
Abstract: We propose a general framework for distribution-free nonparametric testing in multi-dimensions, based on a notion of multivariate ranks defined using the theory of optimal transport (see e.g., Villani (2003)). We demonstrate the applicability of this approach by constructing exactly distribution-free tests for two classical nonparametric problems: (i) testing for the equality of two multivariate distributions, and (ii) testing for mutual independence between two random vectors. In particular, we propose (multivariate) rank versions of Hotelling T^2 and kernel two-sample tests (e.g., Gretton et al. (2012), Szekely and Rizzo (2013)), and kernel tests for independence (e.g., Gretton et al. (2007), Szekely et al. (2007)) for scenarios (i) and (ii) respectively. We investigate the consistency and asymptotic distributions of these tests, both under the null and local contiguous alternatives. We also study the local power and asymptotic (Pitman) efficiency of these multivariate tests (based on optimal transport), and show that a subclass of these tests achieve attractive efficiency lower bounds that mimic the remarkable efficiency results of Hodges and Lehmann (1956) and Chernoff and Savage (1958) (for the Wilcoxon-rank sum test). To the best of our knowledge, these are the first collection of multivariate, nonparametric, exactly distribution-free tests that provably achieve such attractive efficiency lower bounds. We also study the rates of convergence of the rank maps (aka optimal transport maps).