Related papers: Neural Wasserstein Two-Sample Tests
Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…
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…
Wasserstein autoregression provides a robust framework for modeling serial dependence among probability distributions, with wide-ranging applications in economics, finance, and climate science. In this paper, we develop portmanteau-type…
Wasserstein barycenters provide a geometrically meaningful way to aggregate probability distributions, built on the theory of optimal transport. They are difficult to compute in practice, however, leading previous work to restrict their…
The problem of modeling the relationship between univariate distributions and one or more explanatory variables has found increasing interest. Traditional functional data methods cannot be applied directly to distributional data because of…
Measuring similarities between different tasks is critical in a broad spectrum of machine learning problems, including transfer, multi-task, continual, and meta-learning. Most current approaches to measuring task similarities are…
The Wasserstein distance quantifies the distance between two probability measures on a metric space. We prove an analogue of the Berry-Esseen inequality for the Wasserstein distance on a finite area hyperbolic surface. This inequality…
Diffusion models accomplish remarkable success in data generation tasks across various domains. However, the iterative sampling process is computationally expensive. Consistency models are proposed to learn consistency functions to map from…
We study high-dimensional two-sample mean comparison and address the curse of dimensionality through data-adaptive projections. Leveraging the low-dimensional and localized signal structures commonly seen in single-cell genomics data, our…
We study a class of distributionally robust games where agents are allowed to heterogeneously choose their risk aversion with respect to distributional shifts of the uncertainty. In our formulation, heterogeneous Wasserstein ball…
Generative modeling aims to produce new random examples from an unknown target distribution, given access to a finite collection of examples. Among the leading approaches, denoising diffusion probabilistic models (DDPMs) construct such…
In this work, we look at Score-based generative models (also called diffusion generative models) from a geometric perspective. From a new view point, we prove that both the forward and backward process of adding noise and generating from…
Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system. This invariance is powerful, but discrete GW is a nonconvex quadratic optimal transport…
We introduce and study a novel model-selection strategy for Bayesian learning, based on optimal transport, along with its associated predictive posterior law: the Wasserstein population barycenter of the posterior law over models. We first…
We consider sampling from a Gibbs distribution by evolving finitely many particles. We propose a preconditioned version of a recently proposed noise-free sampling method, governed by approximating the score function with the numerically…
Score matching provides an effective approach to learning flexible unnormalized models, but its scalability is limited by the need to evaluate a second-order derivative. In this paper, we present a scalable approximation to a general family…
Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their…
The adapted Wasserstein distance controls the calibration errors of optimal values in various stochastic optimization problems, pricing and hedging problems, optimal stopping problems, etc. However, statistical aspects of the adapted…
The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive…
In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We…