Conditional Simulation via Entropic Optimal Transport

This conference talk by Ricardo Baptista from the California Institute of Technology explores "Conditional simulation via entropic optimal transport" presented at IPAM's Statistical and Numerical Methods for Non-commutative Optimal Transport Workshop at UCLA. Dive into the fundamental challenge of conditional simulation in statistical modeling, which involves generating samples from conditionals given finite data points from a joint distribution. Learn about a promising approach using conditional Brenier maps, where map components pushforward a reference distribution to conditionals of the target. Discover a proposed non-parametric estimator for conditional Brenier maps that leverages entropic optimal transport's computational scalability. Understand how this estimator builds on Carlier et al.'s 2010 finding that optimal transport maps under rescaled quadratic cost asymptotically converge to conditional Brenier maps. Explore heuristic justifications for selecting scaling parameters based on sample numbers through characterization of the Gaussian setting. Compare this estimator's performance against other machine learning and non-parametric approaches on benchmark datasets and Bayesian inference problems.