相关论文: One dimensional martingale rearrangement couplings
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…
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…
We present a novel multiscale framework for analyzing sequences of probability measures in Wasserstein spaces over Euclidean domains. Exploiting the intrinsic geometry of optimal transport, we construct a multiscale transform applicable to…
We solve constrained optimal transport problems in which the marginal laws are given by the laws of solutions of stochastic differential equations (SDEs). We consider SDEs with irregular coefficients, making only minimal regularity…
This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex…
We study the convergence of divergence-regularized optimal transport as the regularization parameter vanishes. Sharp rates for general divergences including relative entropy or $L^{p}$ regularization, general transport costs and…
We develop a numerical method for the martingale analogue of the Benamou--Brenier optimal transport problem, which seeks a martingale interpolating two prescribed marginals which is closest to the Brownian motion. Recent contributions have…
We propose a unified data-driven framework based on inverse optimal transport that can learn adaptive, nonlinear interaction cost function from noisy and incomplete empirical matching matrix and predict new matching in various matching…
We study the problem of model aggregation within the Wasserstein space for probability measures on the real line. Given a fixed finite collection of candidate probability models, we consider the associated class of Wasserstein barycenters…
Contraction in Wasserstein 1-distance with explicit rates is established for generalized Hamiltonian Monte Carlo with stochastic gradients under possibly nonconvex conditions. The algorithms considered include splitting schemes of kinetic…
We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal…
This paper focuses on computing the convex conjugate (also known as the Legendre-Fenchel conjugate or c-transform) that appears in Euclidean Wasserstein-2 optimal transport. This conjugation is considered difficult to compute and in…
Optimal Transport (OT) metrics allow for defining discrepancies between two probability measures. Wasserstein distance is for longer the celebrated OT-distance frequently-used in the literature, which seeks probability distributions to be…
The Wasserstein barycenter (WB) is an important tool for summarizing sets of probability measures. It finds applications in applied probability, clustering, image processing, etc. When the measures' supports are finite, computing a…
In this paper, we study the stability of the shadow, a projection of a measure onto the set of couplings with respect to the Wasserstein distance. The shadow was introduced by \citet{Eckstein_Nutz_2022} to analyze the stability of the…
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…
Optimization over the space of probability measures endowed with the Wasserstein-2 geometry is central to modern machine learning and mean-field modeling. However, traditional methods relying on full Wasserstein gradients often suffer from…
In this short note, we show that given a cost function $c$, any coupling $\pi$ of two probability measures where the second is a discrete measure can be associated to a certain bipartite graph containing a perfect matching, based on the…
We propose an efficient federated dual decomposition algorithm for calculating the Wasserstein barycenter of several distributions, including choosing the support of the solution. The algorithm does not access local data and uses only…
We study the multivariate deconvolution problem of recovering the distribution of a signal from independent and identically distributed observations additively contaminated with random errors (noise) from a known distribution. For errors…