Related papers: A minimax approach to duality for linear distribut…

Methods that align distributions by minimizing an adversarial distance between them have recently achieved impressive results. However, these approaches are difficult to optimize with gradient descent and they often do not converge well…

Suppose we are given access to $n$ independent samples from distribution $\mu$ and we wish to output one of them with the goal of making the output distributed as close as possible to a target distribution $\nu$. In this work we show that…

This paper studies topological duals of Banach function spaces (BFS). We assume a finite measure but our arguments extend to general locally convex function spaces whose topology is generated by seminorms that satisfy the usual BFS axioms.…

By using the fact that the space of all probability measures with finite support can be somehow completed in two different fashions, one generating the Arens-Eells space and another generating the Kantorovich-Wasserstein (Wasserstein-1)…

Reproducing Kernel Hilbert Space (RKHS) embedding of probability distributions has proved to be an effective approach, via MMD (maximum mean discrepancy), for nonparametric hypothesis testing problems involving distributions defined over…

This paper presents a computationally efficient method for binary classification using Manski's (1975,1985) maximum score model when covariates are discretely distributed and parameters are partially but not point identified. We establish…

In this paper, we present a rigorous framework for rational minimax approximation of matrix-valued functions that generalizes classical scalar approximation theory. Given sampled data $\{(x_\ell, {F}(x_\ell))\}_{\ell=1}^m$ where…

We consider the closeness testing problem for discrete distributions. The goal is to distinguish whether two samples are drawn from the same unspecified distribution, or whether their respective distributions are separated in $L_1$-norm. In…

We consider dual optimization problems to the fundamental problem of finding the minimum distance from a point to a subspace. We provide a counterexample to a theorem which has appeared in the literature, relating the minimum distance…

We analyze several problems of Optimal Transport Theory in the setting of Ergodic Theory. In a certain class of problems we consider questions in Ergodic Transport which are generalizations of the ones in Ergodic Optimization. Another class…

We study the problem of estimating the joint probability mass function (pmf) over two random variables. In particular, the estimation is based on the observation of $m$ samples containing both variables and $n$ samples missing one fixed…

This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex…

We consider the problem of sparsity testing in the high-dimensional linear regression model. The problem is to test whether the number of non-zero components (aka the sparsity) of the regression parameter $\theta^*$ is less than or equal to…

We show that in any complete metric space the probability measures $\mu$ with compact and connected support are the ones having the property that the optimal tranportation distance to any other probability measure $\nu$ living on the…

A recent paper by Cordero-Erausquin and Klartag provides a characterization of the measures $\mu$ on $\R^d$ which can be expressed as the moment measures of suitable convex functions $u$, i.e. are of the form $(\nabla u)\_\\#e^{- u}$ for…

The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…

The paper deals with minimax optimal statistical tests for two composite hypotheses, where each hypothesis is defined by a non-parametric uncertainty set of feasible distributions. It is shown that for every pair of uncertainty sets of the…

While first-order optimization methods are usually designed to efficiently reduce the function value $f(x)$, there has been recent interest in methods efficiently reducing the magnitude of $\nabla f(x)$, and the findings show that the two…

We present an alternative proof of Sanov's theorem for Polish spaces in the weak topology that follows via discretization arguments. We combine the simpler version of Sanov's Theorem for discrete finite spaces and well chosen finite…

We present a general duality result for Wasserstein distributionally robust optimization that holds for any Kantorovich transport cost, measurable loss function, and nominal probability distribution. Assuming an interchangeability principle…