From the 1 of 23 linked papers with an AI index.
23 papers
The Objective Is the Bottleneck: Latent World Models Encode What Their Planners Cannot Use
Joyjeet Singh
Latent world models are judged by how well they predict, so when planning fails at long horizons the natural reading is that the predictor degrades. On a reproduction of LeWorldMod…
Empirical optimal transport potentials: fast rates and a functional central limit theorem
Alberto González-Sanz, Gilles Mordant, Shunan Sheng
Optimal transport potentials are fundamental objects in statistics, economics, and machine learning: their gradients generate optimal transport maps, while the potentials themselve…
The Influence Function of Transport-based Quantiles
Alberto González-Sanz, Shunan Sheng, Bohan Wu +1
Transport-based quantiles extend univariate quantiles to multivariate distributions via optimal transport. We study the influence function of the transport quantile map $\mathbf{Q}…
Sharp Asymptotics for Regularized Optimal Transport
Carlos Cardoso-Perelló, Alberto González-Sanz, Marcel Nutz
We study the small-regularization limit for -regularized optimal transport with and for entropically regularized optimal transport (EOT). The exact first-order (r…
Distributional Limit Theory for Optimal Transport
Eustasio del Barrio, Alberto González-Sanz, Jean-Michel Loubes +1
The paper surveys recent theoretical results on the statistical behavior of empirical optimal transport quantities, such as plans, maps, and costs, and discusses how to construct c…
Finite-sample bounds for regularized optimal transport
Alberto González-Sanz, Marcel Nutz, Austin J. Stromme
We study the sample complexity of regularized optimal transport for general convex regularizations including the Kullback--Leibler divergence and penalties. Our main results…