Constrained Denoising, Optimal Transport, and Empirical Bayes

Watch this 49-minute lecture by Bodhisattva Sen from Columbia University exploring constrained denoising, optimal transport, and empirical Bayes methods presented at IPAM's Statistical and Numerical Methods for Non-commutative Optimal Transport Workshop. Delve into how Bayes and empirical Bayes methods in denoising problems tend to "overshrink" outputs relative to latent variables, and discover a framework that addresses this through variance constraints, distribution constraints, and other constraint types. Learn how recent developments in optimal transport provide a general empirical Bayes framework for estimating optimal constrained denoisers, complete with asymptotic and non-asymptotic convergence guarantees. Examine applications to both simulated and real data in this technical presentation recorded on May 20, 2025, at the Institute for Pure & Applied Mathematics (IPAM) at UCLA.