Related papers: Fast Algorithms for Computational Optimal Transpor…
Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability…
We propose a fundamental metric for measuring the distance between two distributions. This metric, referred to as the decision-focused (DF) divergence, is tailored to stochastic linear optimization problems in which the objective…
Aggregating data from multiple sources can be formalized as an Optimal Transport (OT) barycenter problem, which seeks to compute the average of probability distributions with respect to OT discrepancies. However, in real-world scenarios,…
Optimal transportation theory and the related $p$-Wasserstein distance ($W_p$, $p\geq 1$) are widely-applied in statistics and machine learning. In spite of their popularity, inference based on these tools has some issues. For instance, it…
Computing optimal transport (OT) distances such as the earth mover's distance is a fundamental problem in machine learning, statistics, and computer vision. In this paper, we study the problem of approximating the general OT distance…
In this work, we provide faster algorithms for approximating the optimal transport distance, e.g. earth mover's distance, between two discrete probability distributions $\mu, \nu \in \Delta^n$. Given a cost function $C : [n] \times [n] \to…
Distributed distribution comparison aims to measure the distance between the distributions whose data are scattered across different agents in a distributed system and cannot even be shared directly among the agents. In this study, we…
We consider a distributionally robust second-order stochastic dominance constrained optimization problem. We require the dominance constraints hold with respect to all probability distributions in a Wasserstein ball centered at the…
Computing the Wasserstein barycenter of a set of probability measures under the optimal transport metric can quickly become prohibitive for traditional second-order algorithms, such as interior-point methods, as the support size of the…
We research relations between optimal transport theory (OTT) and approximate Bayesian computation (ABC) possibly connected to relevant metrics defined on probability measures. Those of ABC are computational methods based on Bayesian…
Inspired by recent advances in distributed algorithms for approximating Wasserstein barycenters, we propose a novel distributed algorithm for this problem. The main novelty is that we consider time-varying computational networks, which are…
We study the problem of robust distribution estimation under the Wasserstein distance, a popular discrepancy measure between probability distributions rooted in optimal transport (OT) theory. Given $n$ samples from an unknown distribution…
With the increasing availability of data objects in the form of probability distributions, there is a growing need for statistical methods tailored to distributional data. Distance measures, especially the pairwise distance matrix between…
Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When…
Optimal transport (OT) and the related Wasserstein metric (W) are powerful and ubiquitous tools for comparing distributions. However, computing pairwise Wasserstein distances rapidly becomes intractable as cohort size grows. An attractive…
In this paper we consider convergence rate problems for stochastic strongly-convex optimization in the non-Euclidean sense with a constraint set over a time-varying multi-agent network. We propose two efficient non-Euclidean stochastic…
We study a stochastic first order primal-dual method for solving convex-concave saddle point problems over real reflexive Banach spaces using Bregman divergences and relative smoothness assumptions, in which we allow for stochastic error in…
We consider synthesis and analysis of probability measures using the entropy-regularized Wasserstein-2 cost and its unbiased version, the Sinkhorn divergence. The synthesis problem consists of computing the barycenter, with respect to these…
Motivated, in particular, by the entropy-regularized optimal transport problem, we consider convex optimization problems with linear equality constraints, where the dual objective has Lipschitz $p$-th order derivatives, and develop two…
The 2-Wasserstein distance (or RMS distance) is a useful measure of similarity between probability distributions that has exciting applications in machine learning. For discrete distributions, the problem of computing this distance can be…