相关论文: An optimal transportation approach for assessing a…

We introduce the Gaussian transform (GT), an optimal transport inspired iterative method for denoising and enhancing latent structures in datasets. Under the hood, GT generates a new distance function (GT distance) on a given dataset by…

In this work, we discuss the task of finding a direction of optimal descent for problems in Shape Optimisation and its relation to the dual problem in Optimal Transport. This link was first observed in a previous work which sought…

Gromov--Wasserstein optimal transport (GWOT) aligns metric measure spaces by matching their within-domain relational structures, but large-scale GWOT remains challenging because its objective is nonconvex and projection onto the transport…

We consider learning in an adversarial environment, where an $\varepsilon$-fraction of samples from a distribution $P$ are arbitrarily modified (global corruptions) and the remaining perturbations have average magnitude bounded by $\rho$…

Stochastic ordering among distributions has been considered in a variety of scenarios. Economic studies often involve research about the ordering of investment strategies or social welfare. However, as noted in the literature, stochastic…

The Gromov-Wasserstein (GW) distance is an extension of the optimal transport problem that allows one to match objects between incomparable spaces. At its core, the GW distance is specified as the solution of a non-convex quadratic program…

Optimal transport has recently proved to be a useful tool in various machine learning applications needing comparisons of probability measures. Among these, applications of distributionally robust optimization naturally involve Wasserstein…

The mathematical forces at work behind Generative Adversarial Networks raise challenging theoretical issues. Motivated by the important question of characterizing the geometrical properties of the generated distributions, we provide a…

We introduce a novel optimal transport framework for probabilistic circuits (PCs). While it has been shown recently that divergences between distributions represented as certain classes of PCs can be computed tractably, to the best of our…

Discrepancy measures between probability distributions, often termed statistical distances, are ubiquitous in probability theory, statistics and machine learning. To combat the curse of dimensionality when estimating these distances from…

Many applications of computer vision rely on the alignment of similar but non-identical images. We present a fast algorithm for aligning heterogeneous images based on optimal transport. Our approach combines the speed of fast Fourier…

Optimal transport (OT), and in particular the Wasserstein distance, has seen a surge of interest and applications in machine learning. However, empirical approximation under Wasserstein distances suffers from a severe curse of…

We study stochastic zeroth-order optimization with decision-dependent distributions, where the sampling law depends on the current decision and only noisy function values are available. For the non-smooth non-convex setting, we establish an…

This paper presents a novel Wasserstein distributionally robust control and state estimation algorithm for partially observable linear stochastic systems, where the probability distributions of disturbances and measurement noises are…

Wasserstein distances are widely used in modern data analysis but pose significant computational and statistical challenges in high dimensions. The sliced Wasserstein distance alleviates these challenges by leveraging one-dimensional…

In this paper, we study stochastic non-convex optimization with non-convex random functions. Recent studies on non-convex optimization revolve around establishing second-order convergence, i.e., converging to a nearly second-order optimal…

Measuring dependence between random variables is a fundamental problem in Statistics, with applications across diverse fields. While classical measures such as Pearson's correlation have been widely used for over a century, they have…

In machine learning and computer vision, optimal transport has had significant success in learning generative models and defining metric distances between structured and stochastic data objects, that can be cast as probability measures. The…

We propose a novel fused Gromov-Wasserstein alignment method to jointly learn the Hawkes processes in different event spaces, and align their event types. Given two Hawkes processes, we use fused Gromov-Wasserstein discrepancy to measure…

The quadratically regularized optimal transport problem is empirically known to have sparse solutions: its optimal coupling $\pi_{\varepsilon}$ has sparse support for small regularization parameter $\varepsilon$, in contrast to entropic…