Speaker: Akshay Krishnamurthy
Abstract: I will cover some of my recent progress on the structured normal means problem. In this problem, there is a finite collection of vectors available to the learner, nature chooses one of them and shows the learner a gaussian centered at the chosen vector. The goal of the learner is to identify which vector was chosen with low minimax probability of error. In the first part of the talk, I will focus on the issue of minimax optimality, where I will show nearly-matching upper and lower bounds on the minimax risk, generically for any structured normal means problem. I will also mention an algorithm to precisely characterize the minimax risk and identify a minimax estimator. In the second part of the talk, I will discuss issues of passive and adaptive sampling in the structured normal means problem. I will present a number of well-studied examples throughout.