Related papers: Entropy Regularized Optimal Transport Independence…
We establish a fundamental connection between optimal structure learning and optimal conditional independence testing by showing that the minimax optimal rate for structure learning problems is determined by the minimax rate for conditional…
We study the sample complexity of entropic optimal transport in high dimensions using computationally efficient plug-in estimators. We significantly advance the state of the art by establishing dimension-free, parametric rates for…
We propose new concepts in order to analyze and model the dependence structure between two time series. Our methods rely exclusively on the order structure of the data points. Hence, the methods are stable under monotone transformations of…
In this paper, we address the problem of testing independence between two high-dimensional random vectors. Our approach involves a series of max-sum tests based on three well-known classes of rank-based correlations. These correlation…
Maximum entropy method is a constructive criterion for setting up a probability distribution maximally non-committal to missing information on the basis of partial knowledge, usually stated as constrains on expectation values of some…
Hypothesis tests are a crucial statistical tool for data mining and are the workhorse of scientific research in many fields. Here we study differentially private tests of independence between a categorical and a continuous variable. We take…
For testing two random vectors for independence, we consider testing whether the distance of one vector from a center point is independent from the distance of the other vector from a center point by a univariate test. In this paper we…
Analyzing and controlling system entropy is a powerful tool for regulating predictability of control systems. Applications benefiting from such approaches range from reinforcement learning and data security to human-robot collaboration. In…
We show that the stochastic independence of real-valued random variables is equivalent to the conditional uncorrelation, where the conditioning takes place over the Cartesian products of intervals. Next, we express the mutual independence…
Entropic independence is a structural property of measures that underlies modern proofs of functional inequalities, notably (modified) log-Sobolev inequalities, via ``annealing'' or local-to-global schemes. Existing sufficient criteria for…
For probability measures on countable spaces we derive distributional limits for empirical entropic optimal transport quantities. More precisely, we show that the empirical optimal transport plan weakly converges to a centered Gaussian…
In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min…
We introduce the concepts of dependence and independence in a very general framework. We use a concept of rank to study dependence and independence. By means of the rank we identify (total) dependence with inability to create more…
The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems, by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and…
Learning causal relations from observational data is a fundamental problem with wide-ranging applications across many fields. Constraint-based methods infer the underlying causal structure by performing conditional independence tests.…
We introduce a new measure of interdependence among the components of a random vector along the main diagonal of the vector copula, i.e. along the line $u_{1}=\ldots=u_{J}$, for $\left(u_{1},\ldots,u_{J}\right)\in\left[0,1\right]^{J}$. Our…
Ensuring Conditional Independence (CI) constraints is pivotal for the development of fair and trustworthy machine learning models. In this paper, we introduce \sys, a framework that harnesses optimal transport theory for data repair under…
We use the entropy method to analyze the nonlinear dynamics and stability of a continuum kinetic model of an active nematic suspension. From the time evolution of the relative entropy -- an energy-like quantity in the kinetic model -- we…
The method of maximum entropy is quite a powerful tool to solve the generalized moment problem, which consists of determining the probability density of a random variable X from the knowledge of the expected values of a few functions of the…
Testing for independence between graphs is a problem that arises naturally in social network analysis and neuroscience. In this paper, we address independence testing for inhomogeneous Erd\H{o}s-R\'{e}nyi random graphs on the same vertex…