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

About

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.

Ricardo Baptista, Bamdad Hosseini, Nikola B. Kovachki, Youssef Marzouk · 2020

Related benchmarks

Task	Dataset	Result
Simulation-Based Inference	SBIBM Gaussian Linear	C2ST0.85	19
Simulation-Based Inference	Gaussian Linear	Computation Time (s)0.01	8
Simulation-Based Inference	Gaussian Mixture	Computation Time (s)0.01	8
Simulation-Based Inference	Bernoulli GLM	Computation Time (s)0.01	8
Simulation-Based Inference	Two Moons	Computation Time (s)0.01	8
Simulation-Based Inference	SLCP	Inference Time (s)0.01	8
Posterior Sampling	SLCP SBI benchmark	C2ST98	7
Posterior Sampling	Gaussian Mixture SBI benchmark	C2ST73	7
Posterior Sampling	Bernoulli GLM SBI	C2ST84	7
Posterior Sampling	Two Moons SBI benchmark	C2ST67	6