Shivam Nadimpalli, Columbia University

Abstract

We introduce a new notion of influence—called "convex influence"—for convex sets over Gaussian space which has many of the properties of influences of Boolean functions over the hypercube. Our main results for convex influences give Gaussian space analogues of many important results on influences for monotone Boolean functions, including the Kahn-Kalai-Linial theorem, a sharp threshold theorem of Kalai, and a quantitative correlation inequality due to Talagrand. Time permitting, we will also discuss a recent application of convex influences to the problem of testing convex truncation, a natural algorithmic task in high-dimensional statistics. 

Based on joint works with Anindya De and Rocco A. Servedio.

See: https://sites.google.com/view/rutgersdmseminar