NOTE: This talk will be virtual only by Zoom.
Click the button below or go to: https://yale.zoom.us/j/98072079047
Abstract: Optimal transport is a branch of mathematics which has received a recent surge of interest as a methodological tool in statistics. This field grew out of the optimal transport problem, which seeks to find a transformation between two given probability distributions with minimal expected displacement. Such a transformation is called an optimal transport map, and its expected displacement defines a metric between the two distributions called the Wasserstein distance. Although these two objects appear prominently in a wide range of recent statistical methodologies and applications, the fundamental question of performing statistical inference for these objects remains unsolved in general dimension. In this talk, I will share some of our recent progress in addressing this problem. First, I will present a pointwise central limit theorem for optimal transport maps between distributions with smooth densities. Second, I will explain how these ideas can be used to construct semiparametric efficient estimators of the Wasserstein distance in general dimension. Third, I will present two vignettes of my ongoing interdisciplinary work in experimental high energy physics and super-resolution microscopy, which raise exciting new inferential questions for various optimal transport functionals.
NOTE: This talk will be virtual only by Zoom. Click the above or go to: https://yale.zoom.us/j/98072079047
Speaker Bio: Tudor Manole is a PhD candidate in the Department of Statistics and Data Science at Carnegie Mellon University (CMU), advised by Sivaraman Balakrishnan and Larry Wasserman. He is broadly interested in nonparametric statistics, and has worked on statistical aspects of optimal transport theory, the analysis of finite mixture models, and applications in high energy physics. He was a recipient of the CMU Graduate Presidential Fellowship, and the IMS Lawrence D. Brown Award.