Title:

Recent advances in Empirical Bayes: statistical and optimization perspectives

Abstract:

Introduced by Robbins in the 1950s, Empirical Bayes is a powerful approach and popular framework for large-scale inference that aims at learning and adapting to latent structure in data, by finding data-driven estimators to compete with the Bayesian oracle that knows the true prior. This talk surveys some recent theoretical, methodological, and algorithmic advances in empirical Bayes, in both classical sequence models and extensions where latent variables and data interact through more complex designs. A central theme of this talk is the nonparametric maximum likelihood estimator of Kiefer and Wolfowitz. Along the way, various open problems in the theory and practice of empirical Bayes will be discussed.

This talk is based on joint works with Zhou Fan (Yale), Leying Guan (Yale), Soham Jana (Princeton), Yury Polyanskiy (MIT), and Yandi Shen (Yale): https://arxiv.org/abs/2008.08244, https://arxiv.org/abs/2109.03943, https://arxiv.org/abs/2209.01328, https://arxiv.org/abs/2211.12692, https://arxiv.org/abs/2312.12708

Bio:

Yihong Wu is a Professor in the Department of Statistics and Data Science at Yale University. He received his B.E. degree from Tsinghua University in 2006 and Ph.D. degree from Princeton University in 2011. He was a postdoctoral fellow with the Statistics Department in The Wharton School at the University of Pennsylvania from 2011 to 2012 and an assistant professor in the Department of ECE at the University of Illinois at Urbana-Champaign from 2013 to 2015. His research interests are in the theoretical and algorithmic aspects of high-dimensional statistics, information theory, and optimization. He was elected an IMS fellow in 2023 and was a recipient of the NSF CAREER award in 2017 and the Sloan Research Fellowship in Mathematics in 2018.