相关论文: A novel notion of barycenter for probability distr…

This paper presents a computational framework for the concise encoding of an ensemble of persistence diagrams, in the form of weighted Wasserstein barycenters [100], [102] of a dictionary of atom diagrams. We introduce a multi-scale…

Distributional robustness is a promising framework for training deep learning models that are less vulnerable to adversarial examples and data distribution shifts. Previous works have mainly focused on exploiting distributional robustness…

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…

Existing methods to summarize posterior inference for mixture models focus on identifying a point estimate of the implied random partition for clustering, with density estimation as a secondary goal (Wade and Ghahramani, 2018; Dahl et al.,…

We study barycenters of $N$ probability measures on $\mathbb{R}^d$ with respect to the $p$-Wasserstein metric ($1<p<\infty$). We prove that -- $p$-Wasserstein barycenters of absolutely continuous measures are unique, and again absolutely…

We consider a multimarginal optimal transport, which includes as a particular case the Wasserstein barycenter problem. In this problem one has to find an optimal coupling between $m$ probability measures, which amounts to finding a tensor…

In this paper we propose to perform model ensembling in a multiclass or a multilabel learning setting using Wasserstein (W.) barycenters. Optimal transport metrics, such as the Wasserstein distance, allow incorporating semantic side…

We study the problem of efficient compression of a stochastic source of probability distributions. It can be viewed as a generalization of Shannon's source coding problem. It has relation to the theory of common randomness, as well as to…

This paper presents a unified computational framework for the estimation of distances, geodesics and barycenters of merge trees. We extend recent work on the edit distance [106] and introduce a new metric, called the Wasserstein distance…

A simple way of obtaining robust estimates of the "center" (or the "location") and of the "scatter" of a dataset is to use the maximum likelihood estimate with a class of heavy-tailed distributions, regardless of the "true" distribution…

A novel methodology is developed for the solution of the data-driven Monge optimal transport barycenter problem, where the pushforward condition is formulated in terms of the statistical independence between two sets of random variables:…

We study distribution-on-distribution regression problems in which a response distribution depends on multiple distributional predictors. Such settings arise naturally in applications where the outcome distribution is driven by several…

Adapting large-scale foundation models to new domains with limited supervision remains a fundamental challenge due to latent distribution mismatch, unstable optimization dynamics, and miscalibrated uncertainty propagation. This paper…

This paper is concerned with the problem of defining and estimating statistics for distributions on spaces such as Riemannian manifolds and more general metric spaces. The challenge comes, in part, from the fact that statistics such as…

A new Wasserstein multi-element polynomial chaos expansion (WPCE) is proposed, which is inspired by recent advances in computational optimal transport for estimating Wasserstein distances. The developed method combines unsupervised learning…

We study regression problems with distribution-valued responses and mixed distributional and Euclidean predictors. In quadratic cost, the negative gradient of the Kantorovich potential represents, at each source location, the displacement…

We propose a new clustering method based on optimal transportation. We solve optimal transportation with variational principles, and investigate the use of power diagrams as transportation plans for aggregating arbitrary domains into a…

This paper introduces a novel backup strategy for Monte-Carlo Tree Search (MCTS) designed for highly stochastic and partially observable Markov decision processes. We adopt a probabilistic approach, modeling both value and action-value…

We study the problem of network regression, where one is interested in how the topology of a network changes as a function of Euclidean covariates. We build upon recent developments in generalized regression models on metric spaces based on…

We introduce the problem of transporting vector-valued distributions. In this, a salient feature is that mass may flow between vectorial entries as well as across space (discrete or continuous). The theory relies on a first step taken to…