Stat Colloquium: Dr. Rai Bai
George Mason University
Location
Mathematics/Psychology : TBD
Date & Time
February 20, 2026, 11:00 am – 12:00 pm
Description
Title: Implicit and Explicit Deep Learning Models for Latent Density Estimation
Abstract: Mixing (or prior) density estimation is an important problem in machine learning and statistics, especially in empirical Bayes and g-modeling applications. In this talk, we introduce two new deep learning approaches for estimating the latent density in mixture models. First, we introduce Generative Bootstrapping for Nonparametric Maximum Likelihood Estimation (GB-NPMLE), an implicit deep generative process for rapidly generating NPMLE bootstrap estimates. Whereas traditional bootstrapping requires repeated evaluations on resampled data, GB-NPMLE requires only a single evaluation of a novel two-stage optimization algorithm. Second, we introduce Neural-g, an explicit deep learning model which uses a softmax output layer to ensure that the estimated prior is a valid probability density. We establish the universal approximation capabilities of Neural-g and demonstrate its ability to estimate prior densities that are especially challenging to capture, such as those with flat regions, discontinuities, and heavy tails.