October 24, 2017 Theory Seminar 4:00 pm, CS 140

Statistical Hypothesis Testing in the Modern Age

Gautam Kamath

Abstract: Hypothesis testing is one of the most classical problems in statistics: Given samples from a distribution, were they generated according to some model? In the modern age, we face a number of new challenges, including high dimensions, model misspecification, data sensitivity, and small amounts of data in comparison to massive distribution domain sizes. I'll present a series of vignettes on some recent works in distribution testing, which settle classical problems in the field as well as study some new challenges which arise in modern data analysis. Namely:

  1. Testing if a distribution belongs to some family, for instance, monotone or product distributions;
  2. Testing multivariate distributions while avoiding the curse of dimensionality;
  3. Testing in alternative distances;
  4. Testing while maintaining privacy of the samples.

Based on joint works with Jayadev Acharya, Bryan Cai, Nishanth Dikkala, Constantinos Daskalakis, and John Wright.