Related papers: Dynamical Wasserstein Barycenters for Time-series …

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…

This paper provides a method to design an optimal switching sequence for jump linear systems with given Gaussian initial state uncertainty. In the practical perspective, the initial state contains some uncertainties that come from…

This paper studies the statistical estimation of exact Wasserstein barycenters. Existing non-asymptotic results for empirical barycenters exhibit a severe curse of dimensionality. Motivated by the semi-dual formulation of the barycenter…

Given a collection of probability measures, a practitioner sometimes needs to find an "average" distribution which adequately aggregates reference distributions. A theoretically appealing notion of such an average is the Wasserstein…

A novel variational inference based resampling framework is proposed to evaluate the robustness and generalization capability of deep learning models with respect to distribution shift. We use Auto Encoding Variational Bayes to find a…

Hyperspectral satellite images report greenhouse gas concentrations worldwide on a daily basis. While taking simple averages of these images over time produces a rough estimate of relative emission rates, atmospheric transport means that…

We study the fixed-support Wasserstein barycenter problem (FS-WBP), which consists in computing the Wasserstein barycenter of $m$ discrete probability measures supported on a finite metric space of size $n$. We show first that the…

The Boltzmann machine provides a useful framework to learn highly complex, multimodal and multiscale data distributions that occur in the real world. The default method to learn its parameters consists of minimizing the Kullback-Leibler…

We propose a novel method to directly learn a stochastic transition operator whose repeated application provides generated samples. Traditional undirected graphical models approach this problem indirectly by learning a Markov chain model…

We study the problem of estimating a sequence of evolving probability distributions from historical data, where the underlying distribution changes over time in a nonstationary and nonparametric manner. To capture gradual changes, we…

In this work we study systems consisting of a group of moving particles. In such systems, often some important parameters are unknown and have to be estimated from observed data. Such parameter estimation problems can often be solved via a…

Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…

Constructing flexible probability models that respect constraints on key functionals -- such as the mean -- is a fundamental problem in nonparametric statistics. Existing approaches lack systematic tools for enforcing such constraints while…

In the realm of maritime transportation, autonomous vessel navigation in natural inland waterways faces persistent challenges due to unpredictable natural factors. Existing scheduling algorithms fall short in handling these uncertainties,…

I introduce a general, Bayesian method for modelling univariate time series data assumed to be drawn from a continuous, stochastic process. The method accommodates arbitrary temporal sampling, and takes into account measurement…

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…

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…

We construct an efficient primal-dual forward-backward (PDFB) splitting method for computing a class of minimizing movement schemes with nonlinear mobility transport distances, and apply it to computing Wasserstein-like gradient flows. This…

This paper presents a novel Wasserstein distributionally robust control and state estimation algorithm for partially observable linear stochastic systems, where the probability distributions of disturbances and measurement noises are…

In the field of modern high-energy physics research, there is a growing emphasis on utilizing deep learning techniques to optimize event simulation, thereby expanding the statistical sample size for more accurate physical analysis.…