Greedy inference with structure-exploiting lazy maps

We propose a framework for solving high-dimensional Bayesian inference problems using structure-exploiting low-dimensional transport maps or flows. These maps are confined to a low-dimensional subspace (hence, lazy), and the subspace is identified by minimizing an upper bound on the Kullback-Leibler divergence (hence, structured). Our framework provides a principled way of identifying and exploiting low-dimensional structure in an inference problem. It focuses the expressiveness of a transport map along the directions of most significant discrepancy from the posterior, and can be used to build deep compositions of lazy maps, where low-dimensional projections of the parameters are iteratively transformed to match the posterior. We prove weak convergence of the generated sequence of distributions to the posterior, and we demonstrate the benefits of the framework on challenging inference problems in machine learning and differential equations, using inverse autoregressive flows and polynomial maps as examples of the underlying density estimators. * These authors contributed equally to this work. 2 In this paper, we only consider distributions that are absolutely continuous with respect to the Lebesgue measure on R d , and thus will use the notation π to denote both the distribution and its associated density. 34th Conference on Neural Information Processing Systems (NeurIPS 2020),