Related papers: Transport Dependency: Optimal Transport Based Depe…
Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation,…
In this article we show how ideas, methods and results from optimal transportation can be used to study various aspects of the stationary measuresof Iterated Function Systems equipped with a probability distribution. We recover a classical…
In compact settings, the convergence rate of the empirical optimal transport cost to its population value is well understood for a wide class of spaces and cost functions. In unbounded settings, however, hitherto available results require…
Optimal transport (OT) is a versatile framework for comparing probability measures, with many applications to statistics, machine learning, and applied mathematics. However, OT distances suffer from computational and statistical scalability…
Measuring conditional dependencies among the variables of a network is of great interest to many disciplines. This paper studies some shortcomings of the existing dependency measures in detecting direct causal influences or their lack of…
We consider a generalized one-dimensional chain in a periodic potential (the Frenkel-Kontorova model), with dissipative, pulsating (or ratchet) dynamics as a model of transport when the average force on the system is zero. We find lower…
For realistic scale-free networks, we investigate the traffic properties of stochastic routing inspired by a zero-range process known in statistical physics. By parameters $\alpha$ and $\delta$, this model controls degree-dependent hopping…
We consider random i.i.d. samples of absolutely continuous measures on bounded connected domains. We prove an upper bound on the $\infty$-transportation distance between the measure and the empirical measure of the sample. The bound is…
The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…
We consider probability measures on $\mathbb{R}^{\infty}$ and study optimal transportation mappings for the case of infinite Kantorovich distance. Our examples include 1) quasi-product measures, 2) measures with certain symmetric…
We introduce a novel geometric framework for optimal experimental design (OED). Traditional OED approaches, such as those based on mutual information, rely explicitly on probability densities, leading to restrictive invariance properties.…
We introduce a general framework for testing statistical hypotheses for probability measures supported on finite spaces, which is based on optimal transport (OT). These tests are inspired by the analysis of variance (ANOVA) and its…
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…
Spatial association measures for univariate static spatial data are widely used. When the data is in the form of a collection of spatial vectors with the same temporal domain of interest, we construct a measure of similarity between the…
Consider the Monge-Kantorovich problem of transporting densities $\rho_0$ to $\rho_1$ on $\mathbb{R}^d$ with a strictly convex cost function. A popular relaxation of the problem is the one-parameter family called the entropic cost problem.…
Over the last couple of decades, several copula based methods have been proposed in the literature to test for the independence among several random variables. But these existing tests are not invariant under monotone transformations of the…
Pearson's $\rho$ is the most used measure of statistical dependence. It gives a complete characterization of dependence in the Gaussian case, and it also works well in some non-Gaussian situations. It is well known, however, that it has a…
The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied probability, and machine learning. However, existing…
Optimal transport provides an inherently geometric and highly structured framework for studying spaces of probability measures, supplying a rich theoretical toolkit for contemporary statistics, machine learning, and generative modelling. In…
We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…