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A theory of structure is formulated for systems of many structureless classical particles with stable local interactions in Euclidean space. Such systems are shown to have their structure in thermodynamic equilibrium determined exactly by a…

Statistical Mechanics · Physics 2026-02-12 John Çamkıran , Fabian Parsch , Glenn D. Hibbard

Stationary distributions of multivariate diffusion processes have recently been proposed as probabilistic models of causal systems in statistics and machine learning. Motivated by these developments, we study stationary multivariate…

Statistics Theory · Mathematics 2024-08-02 Tobias Boege , Mathias Drton , Benjamin Hollering , Sarah Lumpp , Pratik Misra , Daniela Schkoda

We introduce an independence criterion based on entropy regularized optimal transport. Our criterion can be used to test for independence between two samples. We establish non-asymptotic bounds for our test statistic and study its…

Machine Learning · Statistics 2022-04-21 Lang Liu , Soumik Pal , Zaid Harchaoui

We propose a dynamic model of dependence structure between financial institutions within a financial system and we construct measures for dependence and financial instability. Employing Markov structures of joint credit migrations, our…

Mathematical Finance · Quantitative Finance 2018-09-11 Yu-Sin Chang

We consider the first-order theory of random variables with the probabilistic independence relation, which concerns statements consisting of random variables, the probabilistic independence symbol, logical operators, and existential and…

Information Theory · Computer Science 2021-08-18 Cheuk Ting Li

This paper proposes a new mutual independence test for a large number of high dimensional random vectors. The test statistic is based on the characteristic function of the empirical spectral distribution of the sample covariance matrix. The…

Statistics Theory · Mathematics 2012-05-31 G. M. Pan , J. Gao , Y. Yang , M. Guo

We construct meta-intransitive systems of independent random variables of any finite order from basic tuple of random variables which generalize intransitive dice. Under this construction, the equality of some linear functional is…

Probability · Mathematics 2024-05-07 Alexey V. Lebedev

We study the problem of testing the null hypothesis that X and Y are conditionally independent given Z, where each of X, Y and Z may be functional random variables. This generalises testing the significance of X in a regression model of…

Statistics Theory · Mathematics 2023-09-27 Anton Rask Lundborg , Rajen D. Shah , Jonas Peters

Conditional independence (CI) testing arises naturally in many scientific problems and applications domains. The goal of this problem is to investigate the conditional independence between a response variable $Y$ and another variable $X$,…

Methodology · Statistics 2025-10-07 Adel Javanmard , Mohammad Mehrabi

Inferring the causal structure that links n observables is usually based upon detecting statistical dependences and choosing simple graphs that make the joint measure Markovian. Here we argue why causal inference is also possible when only…

Statistics Theory · Mathematics 2008-04-24 Dominik Janzing , Bernhard Schoelkopf

In this note we prove a large deviation bound on the sum of random variables with the following dependency structure: there is a dependency graph $G$ with a bounded chromatic number, in which each vertex represents a random variable.…

Probability · Mathematics 2007-06-13 Ronen Gradwohl , Amir Yehudayoff

In a previous paper [Pearl and Verma, 1991] we presented an algorithm for extracting causal influences from independence information, where a causal influence was defined as the existence of a directed arc in all minimal causal models…

Artificial Intelligence · Computer Science 2013-03-25 Tom S. Verma , Judea Pearl

Pearl and Dechter (1996) claimed that the d-separation criterion for conditional independence in acyclic causal networks also applies to networks of discrete variables that have feedback cycles, provided that the variables of the system are…

Artificial Intelligence · Computer Science 2011-06-02 R. M. Neal

An algorithm for automated construction of a sparse Bayesian network given an unstructured probabilistic model and causal domain information from an expert has been developed and implemented. The goal is to obtain a network that explicitly…

Artificial Intelligence · Computer Science 2013-04-08 Sampath Srinivas , Stuart Russell , Alice M. Agogino

Free independence is an important tool for studying the structure of operator algebras. It is natural to ask from the model-theoretic standpoint whether free independence is captured well in first-order model theory via the notion of a…

Operator Algebras · Mathematics 2026-02-25 William Boulanger , Jakub Curda , Emma Harvey , Yizhi Li , Jennifer Pi

Compositional graphoids are fundamental discrete structures which appear in probabilistic reasoning, particularly in the area of graphical models. They are semigraphoids which satisfy the Intersection and Composition properties. These…

Information Theory · Computer Science 2026-05-08 Tobias Boege

Constraint-based causal discovery methods leverage conditional independence tests to infer causal relationships in a wide variety of applications. Just as the majority of machine learning methods, existing work focuses on studying…

Machine Learning · Statistics 2024-05-27 Siyuan Guo , Viktor Tóth , Bernhard Schölkopf , Ferenc Huszár

We give a category-theoretic construction of simple and NSOP$_1$-like independence relations in locally finitely presentable categories, and in the more general locally finitely multipresentable categories. We do so by identifying…

Category Theory · Mathematics 2025-06-24 Mark Kamsma , Jiří Rosický

It is well known that conditional independence can be used to factorize a joint probability into a multiplication of conditional probabilities. This paper proposes a constructive definition of inter-causal independence, which can be used to…

Artificial Intelligence · Computer Science 2013-02-28 Nevin Lianwen Zhang , David L Poole

Given a Bayesian network structure (directed acyclic graph), the celebrated d-separation algorithm efficiently determines whether the network structure implies a given conditional independence relation. We show that this changes drastically…

Computational Complexity · Computer Science 2024-05-14 Cheuk Ting Li