Recorded 20 May 2025. Ricardo Baptista of the California Institute of Technology presents "Conditional simulation via entropic optimal transport" at IPAM's Statistical and Numerical Methods for Non-commutative Optimal Transport Workshop. Abstract: Conditional simulation is a fundamental task in statistical modeling: Generate samples from the conditionals given finitely many data points from a joint distribution. One promising approach is to construct conditional Brenier maps, where the components of the map pushforward a reference distribution to conditionals of the target. While many estimators exist, few, if any, come with statistical or algorithmic guarantees. In this presentation, we propose a non-parametric estimator for conditional Brenier maps based on the computational scalability of entropic optimal transport. Our estimator leverages a result of Carlier et al. (2010), which shows that optimal transport maps under a rescaled quadratic cost asymptotically converge to conditional Brenier maps; our estimator is precisely the entropic analogues of these converging maps. We provide heuristic justifications for choosing the scaling parameter in the cost as a function of the number of samples by fully characterizing the Gaussian setting. Lastly, we compare the performance of the estimator to other machine learning and non-parametric approaches on benchmark datasets and Bayesian inference problems. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-iii-statistical-and-numerical-methods-for-non-commutative-optimal-transport/