相关论文: A Simple Boosting Framework for Transshipment

A transshipment problem (G, d, \lambda) is modeled by a directed graph G = (V, E) with weighted vertices d = (d_v | v \in V) and directed edges \lambda = (\lambda_e | e \in E) interpreted as follows: G is a communication or transportation…

Defining meaningful distances between samples in a dataset is a fundamental problem in machine learning. Optimal Transport (OT) lifts a distance between features (the "ground metric") to a geometrically meaningful distance between samples.…

In this paper, we describe a possible generalization of the Wasserstein 2-metric, originally defined on the space of scalar probability densities, to the space of Hermitian matrices with trace one, and to the space of matrix-valued…

The notion of entropy-regularized optimal transport, also known as Sinkhorn divergence, has recently gained popularity in machine learning and statistics, as it makes feasible the use of smoothed optimal transportation distances for data…

Wasserstein distance, which measures the discrepancy between distributions, shows efficacy in various types of natural language processing (NLP) and computer vision (CV) applications. One of the challenges in estimating Wasserstein distance…

The theory of optimal transport of probability measures has wide-ranging applications across a number of different fields, including concentration of measure, machine learning, Markov chains, and economics. The generalisation of optimal…

Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system. This invariance is powerful, but discrete GW is a nonconvex quadratic optimal transport…

Minimum flow decomposition (MFD) is the NP-hard problem of finding a smallest decomposition of a network flow/circulation $X$ on a directed graph $G$ into weighted source-to-sink paths whose superposition equals $X$. We show that, for…

Variational inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one. Recently, boosting variational inference has been proposed as a new paradigm to approximate the posterior by a…

The Wasserstein distance, rooted in optimal transport (OT) theory, is a popular discrepancy measure between probability distributions with various applications to statistics and machine learning. Despite their rich structure and…

This brief note aims to introduce the recent paradigm of distributional robustness in the field of shape and topology optimization. Acknowledging that the probability law of uncertain physical data is rarely known beyond a rough…

We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…

We introduce a novel, geometry-aware distance metric for the family of von Mises-Fisher (vMF) distributions, which are fundamental models for directional data on the unit hypersphere. Although the vMF distribution is widely employed in a…

This work introduces a novel framework for testing topological variability in weighted networks by combining Hodge decomposition with Wasserstein variance minimization. Traditional approaches that analyze raw edge weights are susceptible to…

Wasserstein barycentres represent average distributions between multiple probability measures for the Wasserstein distance. The numerical computation of Wasserstein barycentres is notoriously challenging. A common approach is to use…

We consider the problem of computing a Wasserstein barycenter for a set of discrete probability distributions with finite supports, which finds many applications in areas such as statistics, machine learning and image processing. When the…

In [Q. Liao et al., Commun. Math. Sci., 20(2022)], a linear-time Sinkhorn algorithm is developed based on dynamic programming, which significantly reduces the computational complexity involved in solving optimal transport problems. However,…

We study Fokker--Planck equations with symmetric, positive definite mobility matrices capturing diffusion in heterogeneous environments. A weighted Wasserstein metric is introduced for which these equations are gradient flows. This metric…

The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…

We give algorithms for geometric graph problems in the modern parallel models inspired by MapReduce. For example, for the Minimum Spanning Tree (MST) problem over a set of points in the two-dimensional space, our algorithm computes a…