Event Date
Abstract
We study the problem of learning a high-density region of an arbitrary distribution. Given a target coverage level, and sample access to an arbitrary distribution D, we want to output a confidence set S such that S achieves the desired coverage and the volume of S is as small as possible. We show that this problem is statistically intractable in the most general setting. Then, we restrict our attention to competing with sets from a set family C with bounded VC dimension and provide approximation algorithms to compute a small volume set with desired coverage. (Based on joint work with Chao Gao, Vaidehi Srinivas, and Aravindan Vijayaraghavan: Computing High-Dimensional Confidence Sets for Arbitrary Distributions [COLT 2025] and Volume Optimality in Conformal Prediction with Structured Prediction Sets [ICML 2025].)
Bio
Liren Shan is a research assistant professor at the Toyota Technological Institute at Chicago. He received his Ph.D. in Computer Science from Northwestern University in 2023, advised by Konstantin Makarychev. He has broad interests in theoretical computer science, machine learning, and artificial intelligence. His research focuses on approximation algorithms, graph theory, and algorithmic game theory, with the goal of designing algorithms for data analysis and decision making in real-world.