CSE Community Seminar | April 26, 2024

Abstract

Transport-based density estimation methods are gaining popularity due to their efficiency in generating samples from the target density to be approximated. In this talk, we introduce a sequential framework for constructing a deterministic transport map as the composition of Knothe-Rosenblatt (KR) maps built in a greedy manner. The key ingredient is the introduction of an arbitrary sequence of *bridging densities*, which is used to guide the sequential algorithm. While tempered (or annealed) bridging densities are natural to use in the context of Bayesian inverse problems, diffusion-based bridging densities are more suitable when the target density is known from samples only. To build each of the KR maps, we first estimate the intermediate density using Sum-of-Squares (SoS) density surrogates, and then we analytically extract the KR map of that precomputed approximation. We also propose a convergence analysis of the resulting algorithm with respect to the alpha-divergence, which generalizes previous results from the literature. Additionally, we numerically demonstrate our method on several benchmarks, including Bayesian inference problems and unsupervised learning tasks.