Speaker:   Matthew Li  (MIT)

Title:  Certifiable Low-Dimensional Structure in Bayesian Inference

Abstract: 

While we can simulate complex physical systems with millions of degrees of freedom, inferring these parameters from data is complicated due to their high dimensionality. It would be nice if we could focus only on inferring the subset of parameters which are "informed by data": adopting the Bayesian framework, we take this to mean the parameters which change significantly from the prior distribution to the posterior distribution. In this talk we will discuss a gradient-based construction of a low-dimensional approximation to the posterior distribution which codifies this core idea. In particular, our approximation is furnished with certifiable and computable error guarantees, which we obtain using tools from Markov semigroup theory such as the logarithmic Sobolev inequality and the Poincar\'e inequality. Joint work with Olivier Zahm and Youssef Marzouk.