We consider Bayesian inference for large-scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model, which is often given as a black box or is impractical to differentiate. In this talk I will discuss a new derivative-free algorithm, which utilizes the ideas from Kalman filter, to efficiently solve these inverse problems.

The algorithm can be seen as a derivative-free approximation of the gradient flow under the Fisher-Rao metric. Firstly, I will present a novel functional inequality for the Fisher-Rao gradient flow, leading to a uniform exponential rate of convergence for the gradient flow associated with KL-divergence, as well as for large families of f-divergences. Secondly, I will discuss our Unscented Kalman Inversion algorithm. It can be derived from a Gaussian approximation of the filtering distribution of a mean-field dynamical system. I will demonstrate the effectiveness of this approach in several numerical experiments, which typically converge within O(10) iterations. 

Short Bio:  Jiaoyang Huang is an Assistant Professor of Statistics and Data Science at the University of Pennsylvania. Before that he was a Simons Junior fellow and postdoc at Courant Institute NYU. He obtained a PhD in mathematics from Harvard University in 2019. His research interests include probability theory and its applications to problems from statistics and computer science.