CS Talk
Aram-Alexandre Pooladian
Host: Andre Wibisono
Title: Entropic estimation of optimal transport maps
Abstract:
We develop a computationally tractable method for estimating the optimal mapbetween two distributions over R^d with rigorous finite-sample guarantees. Leveraging an entropic version of Brenier’s theorem, we show that our estimator is easy to compute using Sinkhorn’s algorithm. As a result, unlike current approaches for map estimation, which are slow to evaluate when the dimension or number of samples is large, our approach is parallelizable and extremely efficient even for massive data sets. Under smoothness assumptions on the optimal map, we show that our estimator enjoys comparable statistical performance to other estimators in the literature, but with much lower computational cost. This is joint work with Jonathan Niles-Weed.