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Data represented by probability measures arise as empirical distributions, posterior distributions, and feature-based representations of complex objects. We study heterogeneity in a population of probability measures through the expected…
This paper is concerned with the detection of multiple change-points in the joint distribution of independent categorical variables. The procedures introduced rely on model selection and are based on a penalized least-squares criterion.…
This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If…
Correctly estimating the discrepancy between two data distributions has always been an important task in Machine Learning. Recently, Cuturi proposed the Sinkhorn distance which makes use of an approximate Optimal Transport cost between two…
We study control of constrained linear systems with only partial statistical information about the uncertainty affecting the system dynamics and the sensor measurements. Specifically, given a finite collection of disturbance realizations…
Capturing data from dynamic processes through cross-sectional measurements is seen in many fields, such as computational biology. Trajectory inference deals with the challenge of reconstructing continuous processes from such observations.…
Bipartite quantum entangled systems can exhibit measurement correlations that violate Bell inequalities, revealing the profoundly counter-intuitive nature of the physical universe. These correlations reflect the impossibility of…
The object of this paper is to study estimates of $\epsilon^{-q}W_p(\mu+\epsilon\nu, \mu)$ for small $\epsilon>0$. Here $W_p$ is the Wasserstein metric on positive measures, $p>1$, $\mu$ is a probability measure and $\nu$ a signed, neutral…
We study distributionally robust quantile regression using type-$p$ Wasserstein ambiguity sets. We derive a closed-form expression for the worst-case quantile regression loss under general $p$-Wasserstein uncertainty. We further give a…
Wasserstein autoregression provides a robust framework for modeling serial dependence among probability distributions, with wide-ranging applications in economics, finance, and climate science. In this paper, we develop portmanteau-type…
This article studies a general divide-and-conquer algorithm for approximating continuous one-dimensional probability distributions with finite mean. The article presents a numerical study that compares pre-existing approximation schemes…
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…
The main purpose of this paper is to introduce first a new family of empirical test statistics for testing a simple null hypothesis when the vector of parameters of interest are defined through a specific set of unbiased estimating…
This paper is devoted to the stochastic approximation of entropically regularized Wasserstein distances between two probability measures, also known as Sinkhorn divergences. The semi-dual formulation of such regularized optimal…
Statistical inference can be performed by minimizing, over the parameter space, the Wasserstein distance between model distributions and the empirical distribution of the data. We study asymptotic properties of such minimum Wasserstein…
This paper builds Wasserstein ambiguity sets for the unknown probability distribution of dynamic random variables leveraging noisy partial-state observations. The constructed ambiguity sets contain the true distribution of the data with…
We revisit the question of characterizing the convergence rate of plug-in estimators of optimal transport costs. It is well known that an empirical measure comprising independent samples from an absolutely continuous distribution on…
We propose a new method to estimate Wasserstein distances and optimal transport plans between two probability distributions from samples in high dimension. Unlike plug-in rules that simply replace the true distributions by their empirical…
We propose new goodness-of-fit tests for the Poisson distribution. The testing procedure entails fitting a weighted Poisson distribution, which has the Poisson as a special case, to observed data. Based on sample data, we calculate an…
We provide a distribution-free test that can be used to determine whether any two joint distributions $p$ and $q$ are statistically different by inspection of a large enough set of samples. Following recent efforts from Long et al. [1], we…