相关论文: Wasserstein Contraction of Coordinate Ascent Varia…
As the problem of minimizing functionals on the Wasserstein space encompasses many applications in machine learning, different optimization algorithms on $\mathbb{R}^d$ have received their counterpart analog on the Wasserstein space. We…
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…
Score-based generative modeling with probability flow ordinary differential equations (ODEs) has achieved remarkable success in a variety of applications. While various fast ODE-based samplers have been proposed in the literature and…
The squared Wasserstein distance is a natural quantity to compare probability distributions in a non-parametric setting. This quantity is usually estimated with the plug-in estimator, defined via a discrete optimal transport problem which…
A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation (ABC) has become a popular approach to overcome this issue, in which one simulates…
Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…
Leveraging the Wasserstein distance -- a summation of sample-wise transport distances in data space -- is advantageous in many applications for measuring support differences between two underlying density functions. However, when supports…
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…
A common feature of methods for analyzing samples of probability density functions is that they respect the geometry inherent to the space of densities. Once a metric is specified for this space, the Fr\'echet mean is typically used to…
In this paper, we study statistical inference for the Wasserstein distance, which has attracted much attention and has been applied to various machine learning tasks. Several studies have been proposed in the literature, but almost all of…
We investigate the asymptotic behavior of parametric Bayes estimators under a broad class of loss functions that extend beyond the classical translation-invariant setting. To this end, we develop a unified theoretical framework for loss…
We expound on some known lower bounds of the quadratic Wasserstein distance between random vectors in $\mathbb{R}^n$ with an emphasis on affine transformations that have been used in manifold learning of data in Wasserstein space. In…
A functional for joint variational object segmentation and shape matching is developed. The formulation is based on optimal transport w.r.t. geometric distance and local feature similarity. Geometric invariance and modelling of…
The Wasserstein distance is a metric on a space of probability measures that has seen a surge of applications in statistics, machine learning, and applied mathematics. However, statistical aspects of Wasserstein distances are bottlenecked…
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…
Wasserstein distance induces a natural Riemannian structure for the probabilities on the Euclidean space. This insight of classical transport theory is fundamental for tremendous applications in various fields of pure and applied…
This paper studies the convergence properties of the inexact Jordan-Kinderlehrer-Otto (JKO) scheme and proximal-gradient algorithm in the context of Wasserstein spaces. The JKO scheme, a widely-used method for approximating solutions to…
Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the…
Distributionally-robust optimization is often studied for a fixed set of distributions rather than time-varying distributions that can drift significantly over time (which is, for instance, the case in finance and sociology due to…
We introduce a modified Benamou-Brenier type approach leading to a Wasserstein type distance that allows global invariance, specifically, isometries, and we show that the problem can be summarized to orthogonal transformations. This…