相关论文: Fast and Smooth Interpolation on Wasserstein Space

This paper studies iterative schemes for measure transfer and approximation problems, which are defined through a slicing-and-matching procedure. Similar to the sliced Wasserstein distance, these schemes benefit from the availability of…

In this article we study a variational problem providing a way to extend for all times minimizing geodesics connecting two given probability measures, in the Wasserstein space. This is simply obtained by allowing for negative coefficients…

We propose to study and promote the robustness of a model as per its performance through the interpolation of training data distributions. Specifically, (1) we augment the data by finding the worst-case Wasserstein barycenter on the…

Interpolation of data on non-Euclidean spaces is an active research area fostered by its numerous applications. This work considers the Hermite interpolation problem: finding a sufficiently smooth manifold curve that interpolates a…

This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e. Wasserstein) metrics. These flows have proved useful to tackle theoretically and numerically non-linear diffusion equations that model…

Given a family of probability measures in P(X), the space of probability measures on a Hilbert space X, our goal in this paper is to highlight one ore more curves in P(X) that summarize efficiently that family. We propose to study this…

Squared Wasserstein distance is a frequently used tool to measure discrepancy between probability distributions. This distance is typically computed between empirical measures of size $n$ from two underlying random samples. Unfortunately,…

Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions. Here we consider an alternative, which embeds data as discrete…

This work primarily focuses on providing full implementation details for Worsey-Farin (WF) spline interpolation over tetrahedral elements. While this spline space is not new and the theory has been covered in other works, there is a lack of…

We propose Gaussian optimal transport for Image style transfer in an Encoder/Decoder framework. Optimal transport for Gaussian measures has closed forms Monge mappings from source to target distributions. Moreover interpolates between a…

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…

In a series of papers (Lombardi & Schneider 2001, 2002) we studied in detail the statistical properties of an interpolation technique widely used in astronomy. In particular, we considered the average interpolated map and its covariance…

One of the primary goals of coastal water quality monitoring is to characterize spatial variation. Generally, this monitoring takes place at a limited number of fixed sampling points. The alternative sampling methodology explored in this…

We investigate stochastic interpolation, a recently introduced framework for high dimensional sampling which bears many similarities to diffusion modeling. Stochastic interpolation generates a data sample by first randomly initializing a…

Wasserstein distance (WD) and the associated optimal transport plan have been proven useful in many applications where probability measures are at stake. In this paper, we propose a new proxy of the squared WD, coined min-SWGG, that is…

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.…

Continuous representations are fundamental for modeling sampled data and performing computations and numerical simulations directly on the model or its elements. To effectively and efficiently address the approximation of point clouds we…

We prove general upper estimates for the distance between two Borel probability measures in Wasserstein metric in terms of the Fourier transforms of the measures. We work in compact manifolds including the torus, the Euclidean unit sphere,…

Variational problems that involve Wasserstein distances have been recently proposed to summarize and learn from probability measures. Despite being conceptually simple, such problems are computationally challenging because they involve…

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…