Work

Conditional Sampling with Monotone GANs: From Generative Models to Likelihood-Free Inference

Year: 2024

Type: article

Abstract: . We present a novel framework for conditional sampling of probability measures, using block triangular transport maps. We develop the theoretical foundations of block triangular transport in a Banach space setting, establishing general conditions under which conditional sampling can be achieved and drawing connections between monotone block triangular maps and optimal transport. Based on this theory, we then introduce a computational approach, called monotone generative adversarial networks (M-GANs), to learn suitable block triangular maps. Our algorithm uses only samples from the underlying joint probability measure and is hence likelihood-free. Numerical experiments with M-GAN demonstrate accurate sampling of conditional measures in synthetic examples, Bayesian inverse problems involving ordinary and partial differential equations, and probabilistic image inpainting.

Source: SIAM/ASA Journal on Uncertainty Quantification

DOI: 10.1137/23m1581546

Authors: Ricardo Baptista, Bamdad Hosseini, Nikola B. Kovachki, Youssef M. Marzouk

Institutions: California Institute of Technology, University of Washington, Nvidia (United States), Massachusetts Institute of Technology

Language: English

Topic: Markov Chains and Monte Carlo Methods

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green