相关论文: Hierarchical Low-Rank Approximation of Regularized…
In this paper, we are motivated by two important applications: entropy-regularized optimal transport problem and road or IP traffic demand matrix estimation by entropy model. Both of them include solving a special type of optimization…
The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…
Obtaining solutions to Optimal Transportation (OT) problems is typically intractable when the marginal spaces are continuous. Recent research has focused on approximating continuous solutions with discretization methods based on i.i.d.…
We propose a balanced coarsening scheme for multilevel hypergraph partitioning. In addition, an initial partitioning algorithm is designed to improve the quality of k-way hypergraph partitioning. By assigning vertex weights through the LPT…
This contribution presents substantial computational advancements to compare measures even with varying masses. Specifically, we utilize the nonequispaced fast Fourier transform to accelerate the radial kernel convolution in unbalanced…
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…
The Wasserstein metric is an important measure of distance between probability distributions, with applications in machine learning, statistics, probability theory, and data analysis. This paper provides upper and lower bounds on…
Data unfolding -- the removal of noise or artifacts from measurements -- is a fundamental task across the experimental sciences. Of particular interest are applications in physics, where the dominant approach is Richardson-Lucy (RL)…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
Estimating Wasserstein distances between two high-dimensional densities suffers from the curse of dimensionality: one needs an exponential (wrt dimension) number of samples to ensure that the distance between two empirical measures is…
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…
This paper studies the problem of computing a linear approximation of quadratic Wasserstein distance $W_2$. In particular, we compute an approximation of the negative homogeneous weighted Sobolev norm whose connection to Wasserstein…
Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…
We propose a dense associative memory for empirical measures (weighted point clouds). Stored patterns and queries are finitely supported probability measures, and retrieval is defined by minimizing a Hopfield-style log-sum-exp energy built…
Wasserstein Discriminant Analysis (WDA) is a new supervised method that can improve classification of high-dimensional data by computing a suitable linear map onto a lower dimensional subspace. Following the blueprint of classical Linear…
Computing the empirical Wasserstein distance in the Wasserstein-distance-based independence test is an optimal transport (OT) problem with a special structure. This observation inspires us to study a special type of OT problem and propose a…
We are interested in the Wasserstein distance between two probability measures on $\R^n$ sharing the same copula $C$. The image of the probability measure $dC$ by the vectors of pseudo-inverses of marginal distributions is a natural…
The Sliced-Wasserstein distance (SW) is being increasingly used in machine learning applications as an alternative to the Wasserstein distance and offers significant computational and statistical benefits. Since it is defined as an…
This paper is focused on the study of entropic regularization in optimal transport as a smoothing method for Wasserstein estimators, through the prism of the classical tradeoff between approximation and estimation errors in statistics.…
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…