7 papers
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}…
Bid--Ask Martingale Optimal Transport
Bryan Liang, Marcel Nutz, Shunan Sheng +1
Martingale Optimal Transport (MOT) provides a framework for robust pricing and hedging of illiquid derivatives. Classical MOT enforces exact calibration of model marginals to the m…
Linearization of Monge-Ampère Equations and Statistical Applications
Alberto González-Sanz, Shunan Sheng
Optimal transport has found numerous applications across data science, many of which require differentiating the optimal transport map with respect to the underlying probability de…
Theory and computation for structured variational inference
Shunan Sheng, Bohan Wu, Bennett Zhu +2
Structured variational inference constitutes a core methodology in modern statistical applications. Unlike mean-field variational inference, the approximate posterior is assumed to…
Mode Collapse of Mean-Field Variational Inference
Shunan Sheng, Bohan Wu, Alberto González-Sanz
Mean-field variational inference (MFVI) is a widely used method for approximating high-dimensional probability distributions by product measures. It has been empirically observed t…