Related papers: Bridging multiple worlds: multi-marginal optimal t…
We explore the structure of solutions to a family of non-linear martingale optimal transport (MOT) problems that involve conditional expectations in the objective functional. En route general results concerning optimization over…
Partial identification often arises when the joint distribution of the data is known only up to its marginals. We consider the corresponding partially identified GMM model and develop a methodology for identification, estimation, and…
Optimal transport (OT) based data analysis is often faced with the issue that the underlying cost function is (partially) unknown. This paper is concerned with the derivation of distributional limits for the empirical OT value when the cost…
Optimal transport (OT) is a powerful geometric and probabilistic tool for finding correspondences and measuring similarity between two distributions. Yet, its original formulation relies on the existence of a cost function between the…
Given samples from two joint distributions, we consider the problem of Optimal Transportation (OT) between them when conditioned on a common variable. We focus on the general setting where the conditioned variable may be continuous, and the…
In this paper, we develop a unified approach to study partial identification of a finite-dimensional parameter defined by a general moment model with incomplete data. We establish a novel characterization of the identified set for the true…
We study the problem of estimating latent population flows from aggregated count data. This problem arises when individual trajectories are not available due to privacy issues or measurement fidelity. Instead, the aggregated observations…
Multimarginal optimal transport (MOT) has emerged as a useful framework for many applied problems. However, compared to the well-studied classical two-marginal optimal transport theory, analysis of MOT is far more challenging and remains…
Neural network-based optimal transport (OT) is a recent and fruitful direction in the generative modeling community. It finds its applications in various fields such as domain translation, image super-resolution, computational biology and…
The purpose of this paper is to introduce a new numerical method to solve multi-marginal optimal transport problems with pairwise interaction costs. The complexity of multi-marginal optimal transport generally scales exponentially in the…
Matching on covariates is a well-established framework for estimating causal effects in observational studies. The principal challenge stems from the often high-dimensional structure of the problem. Many methods have been introduced to…
Mini-batch optimal transport (m-OT) has been widely used recently to deal with the memory issue of OT in large-scale applications. Despite their practicality, m-OT suffers from misspecified mappings, namely, mappings that are optimal on the…
Multimarginal optimal transport (MOT) is a powerful framework for modeling interactions between multiple distributions, yet its applicability is bottlenecked by a high computational overhead. Entropic regularization provides computational…
We introduce a constrained optimal transport problem where origins $x$ can only be transported to destinations $y\geq x$. Our statistical motivation is to describe the sharp upper bound for the variance of the treatment effect $Y-X$ given…
Causal estimands can vary significantly depending on the relationship between outcomes in treatment and control groups, potentially leading to wide partial identification (PI) intervals that impede decision making. Incorporating covariates…
We consider a class of stochastic optimal transport, SOT for short, with given two endpoint marginals in the case where a cost function exhibits at most quadratic growth. We first study the upper and lower estimates, the short--time…
The objective in statistical Optimal Transport (OT) is to consistently estimate the optimal transport plan/map solely using samples from the given source and target marginal distributions. This work takes the novel approach of posing…
In this work, we construct a novel numerical method for solving the multi-marginal optimal transport problems with Coulomb cost. This type of optimal transport problems arises in quantum physics and plays an important role in understanding…
In this article we revisit the weak optimal transport (WOT) problem, introduced by Gozlan, Roberto, Samson and Tetali (2017). We work on the real line, with barycentric cost functions, and as our first result give the following…
This paper develops a computational framework for Multi-Period Martingale Optimal Transport (MMOT), addressing convergence rates, algorithmic efficiency, and financial calibration. Our contributions include: (1) Theoretical analysis: We…