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

• URL: http://arxiv.org/abs/2006.06755v3
• Date: Mon, 5 Jun 2023 23:53:27 GMT
• Title: Conditional Sampling with Monotone GANs: from Generative Models to Likelihood-Free Inference
• Authors: Ricardo Baptista, Bamdad Hosseini, Nikola B. Kovachki, Youssef Marzouk
• Abstract summary: 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. We then introduce a computational approach, called monotone generative adversarial networks, to learn suitable block triangular maps.
• Score: 4.913013713982677
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 in-painting.

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