Approximate inference with Wasserstein gradient flows
This addresses computational bottlenecks in high-dimensional domains for researchers in statistics and machine learning, though it is incremental as it builds on existing gradient flow formulations.
The authors tackled the problem of approximate inference for diffusion processes by proposing a discretization-free method based on Wasserstein gradient flows, achieving performance comparable to state-of-the-art on a nonlinear filtering task.
We present a novel approximate inference method for diffusion processes, based on the Wasserstein gradient flow formulation of the diffusion. In this formulation, the time-dependent density of the diffusion is derived as the limit of implicit Euler steps that follow the gradients of a particular free energy functional. Existing methods for computing Wasserstein gradient flows rely on discretization of the domain of the diffusion, prohibiting their application to domains in more than several dimensions. We propose instead a discretization-free inference method that computes the Wasserstein gradient flow directly in a space of continuous functions. We characterize approximation properties of the proposed method and evaluate it on a nonlinear filtering task, finding performance comparable to the state-of-the-art for filtering diffusions.