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We address the problem of efficiently computing Wasserstein distances for multiple pairs of distributions drawn from a meta-distribution. To this end, we propose a fast estimation method based on regressing Wasserstein distance on sliced…
Measuring dependence between random variables is a fundamental problem in Statistics, with applications across diverse fields. While classical measures such as Pearson's correlation have been widely used for over a century, they have…
Markov decision processes (MDPs) are known to be sensitive to parameter specification. Distributionally robust MDPs alleviate this issue by allowing for \emph{ambiguity sets} which give a set of possible distributions over parameter sets.…
Suppose we are given two metric spaces and a family of continuous transformations from one to the other. Given a probability distribution on each of these two spaces - namely the source and the target measures - the Wasserstein alignment…
The Wasserstein barycenter problem seeks a probability measure that minimizes the weighted average of the Wasserstein distances to a given collection of probability measures. We study the discrete setting, where each measure has finite…
We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal…
We consider the bicausal optimal transport problem between the laws of scalar time-homogeneous stochastic differential equations, and we establish the optimality of the synchronous coupling between these laws. The proof of this result is…
This paper is concerned by statistical inference problems from a data set whose elements may be modeled as random probability measures such as multiple histograms or point clouds. We propose to review recent contributions in statistics on…
We study the Wasserstein distance of order 1 between the empirical distribution and the marginal distribution of stationary $\alpha$-dependent sequences. We prove some moments inequalities of order p for any p $\ge$ 1, and we give some…
We consider a class of stochastic gradient optimization schemes. Assuming that the objective function is strongly convex, we prove weak error estimates which are uniform in time for the error between the solution of the numerical scheme,…
We investigate an expected utility maximization problem under model uncertainty in a one-period financial market. We capture model uncertainty by replacing the baseline model $\mathbb{P}$ with an adverse choice from a Wasserstein ball of…
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…
This paper is focused on the study of entropic regularization in optimal transport as a smoothing method for Wasserstein estimators, through the prism of the classical tradeoff between approximation and estimation errors in statistics.…
This paper studies the expected optimal value of a mixed 0-1 programming problem with uncertain objective coefficients following a joint distribution. We assume that the true distribution is not known exactly, but a set of independent…
The standard quadratic optimization problem (StQP) consists of minimizing a quadratic form over the standard simplex. Without assuming convexity or concavity of the quadratic form, the StQP is NP-hard. This problem has many interesting…
We obtain explicit $p$-Wasserstein distance error bounds between the distribution of the multi-parameter MLE and the multivariate normal distribution. Our general bounds are given for possibly high-dimensional, independent and identically…
Statistical models often include thousands of parameters. However, large models decrease the investigator's ability to interpret and communicate the estimated parameters. Reducing the dimensionality of the parameter space in the estimation…
We analyze the sensitivity of solutions to the Fokker-Planck equation with respect to some unknown parameter. Our main result is to provide quantitative upper bounds for the $p$-Wasserstein distance $\mathcal{W}_p$ between two solutions…
We study the continuity properties of optimal solutions to stochastic control problems with respect to initial probability measures and applications of these to the robustness of optimal control policies applied to systems with incomplete…
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…