相关论文: Measure Estimation in the Barycentric Coding Model

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…

In this paper, we consider a probabilistic setting where the probability measures are considered to be random objects. We propose a procedure of construction non-asymptotic confidence sets for empirical barycenters in 2-Wasserstein space…

Collecting and aggregating information from several probability measures or histograms is a fundamental task in machine learning. One of the popular solution methods for this task is to compute the barycenter of the probability measures…

Wasserstein distributionally robust optimization estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance…

The purpose of this paper is to provide a systematic discussion of a generalized barycenter based on a variant of unbalanced optimal transport (UOT) that defines a distance between general non-negative, finitely supported measures by…

Scientific imaging problems are often severely ill-posed, and hence have significant intrinsic uncertainty. Accurately quantifying the uncertainty in the solutions to such problems is therefore critical for the rigorous interpretation of…

We analyze the convex structure of the set of positive operator valued measures (POVMs) representing quantum measurements on a given finite dimensional quantum system, with outcomes in a given locally compact Hausdorff space. The extreme…

We derive first-order (in the stepsize) bounds on the bias in Wasserstein distances of the invariant measure of stochastic gradient kinetic Langevin dynamics with minimal assumptions on the stochastic gradient noise. These bounds sharpen…

In this paper, based on the Fr{\'e}chet mean, we define a notion of barycenter corresponding to a usual notion of statistical mean. We prove the existence of Wasserstein barycenters of random distributions defined on a geodesic space (E,…

This paper concerns the convergence of empirical measures in high dimensions. We propose a new class of probability metrics and show that under such metrics, the convergence is free of the curse of dimensionality (CoD). Such a feature is…

We study the minimax optimal rate for estimating the Wasserstein-$1$ metric between two unknown probability measures based on $n$ i.i.d. empirical samples from them. We show that estimating the Wasserstein metric itself between probability…

The problem of blind identification of channel codes at a receiver involves identifying a code chosen by a transmitter from a known code-family, by observing the transmitted codewords through the channel. Most existing approaches for…

We propose a novel system identification technique, based on a least-mean square algorithm, allowing for the estimation of a linear channel by using an unknown-response measurement channel. The key of the technique is a memoryless nonlinear…

The paper investigates the techniques of quantum computation in metrological predictions, with a particular emphasis on enhancing prediction potential through variational parameter estimation. The applicability of quantum simulations and…

The Hellinger-Kantorovich (HK) distance is an unbalanced extension of the Wasserstein-2 distance. It was shown recently that the HK barycenter exhibits a much more complex behaviour than the Wasserstein barycenter. Motivated by this…

We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…

We show that the problem of finding the barycenter in the Hellinger-Kantorovich setting admits a least-cost soft multi-marginal formulation, provided that a one-sided hard marginal constraint is introduced. The constrained approach is then…

Cooperative geolocation has attracted significant research interests in recent years. A large number of localization algorithms rely on the availability of statistical knowledge of measurement errors, which is often difficult to obtain in…

Change point detection for time series analysis is a difficult and important problem in applied statistics, for which a variety of approaches have been developed in the past several decades. Here, the Wasserstein metric is employed as a…

This article focuses on measurement error in covariates in regression analyses in which the aim is to estimate the association between one or more covariates and an outcome, adjusting for confounding. Error in covariate measurements, if…