Constrained Denoising, Empirical Bayes, and Optimal Transport
In the statistical problem of denoising, Bayes and empirical Bayes methods can "overshrink" their output relative to the latent variables of interest. This work is focused on constrained denoising problems which mitigate such phenomena. At the oracle level, i.e., when the latent variable distribution is assumed known, we apply tools from the theory of optimal transport to characterize the solution to (i) variance-constrained, (ii) distribution-constrained, and (iii) general-constrained denoising problems. At the empirical level, i.e., when the latent variable distribution is not known, we use empirical Bayes methodology to estimate these oracle denoisers. Our approach is modular, and transforms any suitable (unconstrained) empirical Bayes denoiser into a constrained empirical Bayes denoiser. We prove explicit rates of convergence for our proposed methodologies, which both extend and sharpen existing asymptotic results that have previously considered only variance constraints. This is joint work with Adam Jaffe and Nikos Ignatiadis.
BIO: Bodhi Sen is Professor and Chair of Statistics at Columbia University, New York. He completed his Ph.D in Statistics from University of Michigan, Ann Arbor, in 2008. Prior to that, he was a student at the Indian Statistical Institute, Kolkata, where he received his Bachelors (2002) and Masters (2004) in Statistics. His core statistical research centers around nonparametrics --- function estimation (with special emphasis on shape constrained estimation), theory of optimal transport and its applications to statistics, empirical Bayes procedures, kernel methods, likelihood and bootstrap based inference, etc. He is also interested in interdisciplinary research, especially in astronomy. His honors include the NSF CAREER award (2012), and the Young Statistical Scientist Award (YSSA) in the Theory and Methods category from the International Indian Statistical Association (IISA). He is an elected fellow of the Institute of Mathematical Statistics (IMS) and will deliver an IMS medallion lecture in 2026.
