11:30 am–12:30 pm
Jones 303 5747 S. Ellis Ave.
Aravindan Vijayaraghavan
Department of Computer Science
Northwestern University
Title: Finding Small Confidence Sets in High Dimensions
Abstract: Constructing confidence sets is a fundamental problem in statistics: given samples from an arbitrary distribution and a target coverage $1-\alpha$ (e.g., 0.90), the goal is to find a set that covers $1-\alpha$ probability mass while having as small a volume as possible. This task underlies a wide range of applications, including uncertainty quantification and support estimation. Even when restricted to simple geometric families such as Euclidean balls, finding small confidence sets is computationally challenging in high dimensions.
This raises a key question: can we design computationally efficient methods that find these sets with provably near-optimal size?
In this talk, I will present new algorithms that learn confidence balls and confidence ellipsoids with rigorous guarantees of coverage and approximate volume optimality. The algorithms use new connections to robust statistics, convex optimization duality, and the Brascamp-Lieb inequality. Time permitting, I will discuss discrete variants of the problem and their applications to conformal prediction.
Based mostly on joint work with Chao Gao, Liren Shan, and Vaidehi Srinivas.
Bio: Aravindan Vijayaraghavan is the Charles Deering McCormick Professor of Teaching Excellence and Associate Professor of Computer Science at Northwestern University. He is also the Co-Director of the NSF Institute for Data, Econometrics, Algorithms and Learning (IDEAL). His research interests are broadly in algorithms and foundations of data science and machine learning.