Related papers: Decision-Focused Optimal Transport
With the ongoing investment in data collection and communication technology in power systems, data-driven optimization has been established as a powerful tool for system operators to handle stochastic system states caused by weather- and…
An optimal transport (OT) problem seeks to find the cheapest mapping between two distributions with equal total density, given the cost of transporting density from one place to another. Unbalanced OT allows for different total density in…
Fairness concerns are increasingly critical as machine learning models are deployed in high-stakes applications. While existing fairness-aware methods typically intervene at the model level, they often suffer from high computational costs,…
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…
Personalized recommender systems are playing an increasingly important role as more content and services become available and users struggle to identify what might interest them. Although matrix factorization and deep learning based methods…
The adapted Wasserstein distance is a metric for quantifying distributional uncertainty and assessing the sensitivity of stochastic optimization problems on time series data. A computationally efficient alternative to it, is provided by the…
We study multistage distributionally robust linear optimization, where the uncertainty set is defined as a ball of distribution centered at a scenario tree using the nested distance. The resulting minimax problem is notoriously difficult to…
For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the…
When stochastic dominance $F\leq_{st}G$ does not hold, we can improve agreement to stochastic order by suitably trimming both distributions. In this work we consider the $L_2-$Wasserstein distance, $\mathcal W_2$, to stochastic order of…
Optimal transport provides an inherently geometric and highly structured framework for studying spaces of probability measures, supplying a rich theoretical toolkit for contemporary statistics, machine learning, and generative modelling. In…
We discuss the classical problem of measuring the regularity of distribution of sets of $N$ points in $\mathbb{T}^d$. A recent line of investigation is to study the cost ($=$ mass $\times$ distance) necessary to move Dirac measures placed…
We provide theoretical complexity analysis for new algorithms to compute the optimal transport (OT) distance between two discrete probability distributions, and demonstrate their favorable practical performance over state-of-art primal-dual…
A common feature of methods for analyzing samples of probability density functions is that they respect the geometry inherent to the space of densities. Once a metric is specified for this space, the Fr\'echet mean is typically used to…
Metro networks serve as good examples of traffic systems for understanding the relations between geometric structures and transport properties.We study and compare 28 world major metro networks in terms of the Wasserstein distance, the key…
Optimal transport has been used extensively in resource matching to promote the efficiency of resources usages by matching sources to targets. However, it requires a significant amount of computations and storage spaces for large-scale…
Solving large scale Optimal Transport (OT) in machine learning typically relies on sampling measures to obtain a tractable discrete problem. While the discrete solver's accuracy is controllable, the rate of convergence of the discretization…
Distributionally robust supervised learning (DRSL) is emerging as a key paradigm for building reliable machine learning systems for real-world applications -- reflecting the need for classifiers and predictive models that are robust to the…
We propose two distributionally robust optimization (DRO) models for a mobile facility (MF) fleet sizing, routing, and scheduling problem (MFRSP) with time-dependent and random demand, as well as methodologies for solving these models.…
Generative Adversarial Networks (GANs) are one of the most practical methods for learning data distributions. A popular GAN formulation is based on the use of Wasserstein distance as a metric between probability distributions.…
Score-based generative models are shown to achieve remarkable empirical performances in various applications such as image generation and audio synthesis. However, a theoretical understanding of score-based diffusion models is still…