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

Understand

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.