Sumit Mukherjee received his Ph.D at Stanford University, under the supervision of Prof. Persi Diaconis. In Fall 2014, he joined the Department of Statistics at Columbia University as an Assistant Professor. Starting from Fall 2020, has been an Associate Professor at Columbia. Link to Sumit's CV, and Google Scholar page.
His research interests lie in the intersection of Mathematical Statistics, Probability, and Combinatorics. One of his main interests is to develop statistical theory and methods for inference with dependent combinatorial data, such as Ising models and more general discrete Markov random fields, Mallows models on ranking, and exponential random graph models (ERGMs). In another direction he studies persistence (above a level line) for "approximately" stationary Gaussian processes. Sumit also studies limiting distributions of random multilinear/tensor forms arising from graph coloring problems and gratefully acknowledges NSF (DMS-2113414, DMS-1712037) for partially supporting his research.
Talk: When is Naive Mean field accurate?
Abstract: Often in high dimensional Bayesian statistics, the posterior is complicated to work with, and are approximated using variational inference. Possibly the most commonly used and simple method is the naive mean field approximation, which approximates the complicated posterior by a product distribution. In this talk we address the question of when such approximations are valid in a rigorous sense, in the contexts of linear and logistic regressions. Along the way, we develop techniques for various inferential tools, which include estimating the unknown prior in an empirical Bayes setting, and credible intervals with average coverage guarantees.
This is based on joint work with Jiaze Qiu (Harvard), Bodhi Sen (Columbia), and Subhabrata Sen (Harvard).