A0268
Title: Robust Bayesian inference on Riemannian submanifold
Authors: Rong Tang - HKUST (Hong Kong) [presenting]
Abstract: Non-Euclidean spaces routinely arise in modern statistical applications such as medical imaging, robotics, and computer vision, to name a few. While traditional Bayesian approaches are applicable to such settings by considering an ambient Euclidean space as the parameter space, the benefits of integrating manifold structure are demonstrated in the Bayesian framework, both theoretically and computationally. Moreover, existing Bayesian approaches that are designed specifically for manifold-valued parameters are primarily model-based and are typically subject to inaccurate uncertainty quantification under model misspecification. A robust model-free Bayesian inference is proposed for parameters defined on a Riemannian submanifold, which is shown to provide valid uncertainty quantification from a frequentist perspective. Computationally, a Markov chain Monte Carlo is proposed to sample from the posterior on the Riemannian submanifold, where the mixing time, in the large sample regime, is shown to depend only on the intrinsic dimension of the parameter space instead of the potentially much larger ambient dimension.
