Costis Daskalakis
The Challenge of High-Dimensional Statistical Hypothesis Testing

Abstract: How many samples are necessary to distinguish whether a
multi-dimensional distribution is a product measure or 10%-far from
being a product measure in total variation distance? As it turns out,
answering this question rigorously requires exponentially many samples
in the dimension. Similar lower bounds apply to a host of statistical
hypothesis testing problems in high dimensions. So what do we really
know about high-dimensional distributions and the important phenomena
that they model? E.g. what do we really understand about behavior in a
social network, or the output of a Generative Adversarial Network
(GAN)? I will survey recent work on hypothesis testing for
distributions with large support, discuss the challenges arising in
high-dimensional settings, and identify research directions towards
overcoming these challenges.