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The autocovariance and cross-covariance functions naturally appear in many time series procedures (e.g., autoregression or prediction). Under assumptions, empirical versions of the autocovariance and cross-covariance are asymptotically…

We build on the formalism developed in [arXiv:1906.08372v1] to propose new representations of solutions to Stein equations. We provide new uniform and non uniform bounds on these solutions (a.k.a.\ Stein factors). We use these…

We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…

Let F ($\nu$) be the centered Gamma law with parameter $\nu$ > 0 and let us denote by P Y the probability distribution of a random vector Y. We develop a multidimensional variant of the Stein's method for Gamma approximation that allows to…

Consider a set of points sampled independently near a smooth compact submanifold of Euclidean space. We provide mathematically rigorous bounds on the number of sample points required to estimate both the dimension and the tangent spaces of…

Let $\mu_N$ be the empirical measure associated to a $N$-sample of a given probability distribution $\mu$ on $\mathbb{R}^d$. We are interested in the rate of convergence of $\mu_N$ to $\mu$, when measured in the Wasserstein distance of…

The Wasserstein distance between probability measures on compact spaces provides a natural invariant quantitative measure of equidistribution, which is partly similar to the classical discrepancy appearing in Erd\"os-Tur\'an type…

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…

This paper introduces Wasserstein variational inference, a new form of approximate Bayesian inference based on optimal transport theory. Wasserstein variational inference uses a new family of divergences that includes both f-divergences and…

The Wasserstein distance has been an attractive tool in many fields. But due to its high computational complexity and the phenomenon of the curse of dimensionality in empirical estimation, various extensions of the Wasserstein distance have…

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…

We derive normal approximation bounds in the Wasserstein distance for sums of weighted U-statistics, based on a general distance bound for functionals of independent random variables of arbitrary distributions. Those bounds are applied to…

We present a framework for obtaining explicit bounds on the rate of convergence to equilibrium of a Markov chain on a general state space, with respect to both total variation and Wasserstein distances. For Wasserstein bounds, our main tool…

We study the estimation problem of distribution-on-distribution regression, where both predictors and responses are probability measures. Existing approaches typically rely on a global optimal transport map or tangent-space linearization,…

We estimate rates of convergence for empirical measures associated with the subordinated fractional Brownian motion to the uniform distribution on the flat torus under the Wasserstein distance $\mathbb{W}_p$ for all $p\geq1$. In particular,…

We develop a multidimensional Stein methodology for non-degenerate self-decomposable random vectors in $\mathbb{R}^d$ having finite first moment. Building on previous univariate findings, we solve an integro-partial differential Stein…

This paper addresses a new active learning strategy for regression problems. The presented Wasserstein active regression model is based on the principles of distribution-matching to measure the representativeness of the labeled dataset. The…

This paper provides a general framework for Stein's density method for multivariate continuous distributions. The approach associates to any probability density function a canonical operator and Stein class, as well as an infinite…

In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order…

We study the weighted total variation distance between probability measures. Using Fourier-analytic tools, we present estimates in terms of Wasserstein distances between the respective probabilities, under appropriate smoothness and moment…