Related papers: Parameter estimation from aggregate observations: …
Let $\pi\in \Pi(\mu,\nu)$ be a coupling between two probability measures $\mu$ and $\nu$ on a Polish space. In this article we propose and study a class of nonparametric measures of association between $\mu$ and $\nu$, which we call…
The use of high-power industrial equipment, such as large-scale mixing equipment or a hydrocyclone for separation of particles in liquid suspension, demands careful monitoring to ensure correct operation. The fundamental task of…
This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs between two distinct continuous distributions $F$ and $G$ on $\mathbb R$. The estimator is based on the order statistics of (possibly dependent)…
We propose to align distributional data from the perspective of Wasserstein means. We raise the problem of regularizing Wasserstein means and propose several terms tailored to tackle different problems. Our formulation is based on the…
In this article we consider likelihood-based estimation of static parameters for a class of partially observed McKean-Vlasov (POMV) diffusion process with discrete-time observations over a fixed time interval. In particular, using the…
Considering two random variables with different laws to which we only have access through finite size iid samples, we address how to reweight the first sample so that its empirical distribution converges towards the true law of the second…
In this article, we study Wasserstein-type metrics and corresponding barycenters for mixtures of a chosen subset of probability measures called atoms hereafter. In particular, this works extends what was proposed by Delon and Desolneux [A…
We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a…
Scenario reduction techniques are widely applied for solving sophisticated dynamic and stochastic programs, especially in energy and power systems, but also used in probabilistic forecasting, clustering and estimating generative adversarial…
Approximating integrals is a fundamental task in probability theory and statistical inference, and their applied fields of signal processing, and Bayesian learning, as soon as expectations over probability distributions must be computed…
Stein's method has been widely used for probability approximations. However, in the multi-dimensional setting, most of the results are for multivariate normal approximation or for test functions with bounded second- or higher-order…
Methods to extract information from the tracking of mobile objects/particles have broad interest in biological and physical sciences. Techniques based on simple criteria of proximity in time-consecutive snapshots are useful to identify the…
Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…
Comparing probability distributions is at the crux of many machine learning algorithms. Maximum Mean Discrepancies (MMD) and Wasserstein distances are two classes of distances between probability distributions that have attracted abundant…
Sequential Monte Carlo (SMC) samplers are powerful tools for Bayesian inference but suffer from high computational costs due to their reliance on large particle ensembles for accurate estimates. We introduce persistent sampling (PS), an…
Many inference problems involve inferring the number $N$ of components in some region, along with their properties $\{\mathbf{x}_i\}_{i=1}^N$, from a dataset $\mathcal{D}$. A common statistical example is finite mixture modelling. In the…
Wasserstein barycenter, built on the theory of optimal transport, provides a powerful framework to aggregate probability distributions, and it has increasingly attracted great attention within the machine learning community. However, it…
Using the recently developed Sinkhorn algorithm for approximating the Wasserstein distance between probability distributions represented by Monte Carlo samples, we demonstrate exponential filter stability of two commonly used nonlinear…
Bayesian hierarchical modeling is a popular approach to capturing unobserved heterogeneity across individual units. However, standard estimation methods such as Markov chain Monte Carlo (MCMC) can be impracticable for modeling outcomes from…
Motivated by the growing popularity of variants of the Wasserstein distance in statistics and machine learning, we study statistical inference for the Sliced Wasserstein distance--an easily computable variant of the Wasserstein distance.…