Related papers: Conditional independence ideals with hidden variab…

A lattice-theoretic framework is introduced that permits the study of the conditional independence (CI) implication problem relative to the class of discrete probability measures. Semi-lattices are associated with CI statements and a…

Bell inequalities may only be derived, if hidden variables do not depend on the experimental settings. The stochastic independence of hidden and setting variables is called: freedom of choice, free will, measurement independence or no…

Testing for conditional independence is a core aspect of constraint-based causal discovery. Although commonly used tests are perfect in theory, they often fail to reject independence in practice, especially when conditioning on multiple…

Conditional independence in a multivariate normal (or Gaussian) distribution is characterized by the vanishing of subdeterminants of the distribution's covariance matrix. Gaussian conditional independence models thus correspond to algebraic…

Causality lays the foundation for the trajectory of our world. Causal inference (CI), which aims to infer intrinsic causal relations among variables of interest, has emerged as a crucial research topic. Nevertheless, the lack of observation…

Independence screening is a powerful method for variable selection for `Big Data' when the number of variables is massive. Commonly used independence screening methods are based on marginal correlations or variations of it. In many…

We show that there is a general, informative and reliable procedure for discovering causal relations when, for all the investigator knows, both latent variables and selection bias may be at work. Given information about conditional…

The binomial ideal associated with the intersection axiom of conditional probability is shown to be radical and is expressed as intersection of toric prime ideals. This resolves a conjecture in algebraic statistics due to Cartwright and…

Conditional independence (CI) tests are widely used in statistical data analysis, e.g., they are the building block of many algorithms for causal graph discovery. The goal of a CI test is to accept or reject the null hypothesis that $X…

The paper deals with conditional linear information inequalities valid for entropy functions induced by discrete random variables. Specifically, the so-called conditional Ingleton inequalities are in the center of interest: these are valid…

Conditional-independence-based discovery uses statistical tests to identify a graphical model that represents the independence structure of variables in a dataset. These tests, however, can be unreliable, and algorithms are sensitive to…

In many real-world scenarios, interested variables are often represented as discretized values due to measurement limitations. Applying Conditional Independence (CI) tests directly to such discretized data, however, can lead to incorrect…

We introduce binomial edge ideals attached to a simple graph $G$ and study their algebraic properties. We characterize those graphs for which the quadratic generators form a Gr\"obner basis in a lexicographic order induced by a vertex…

Confidence intervals (CIs) are instrumental in statistical analysis, providing a range estimate of the parameters. In modern statistics, selective inference is common, where only certain parameters are highlighted. However, this selective…

It has been postulated that a good representation is one that disentangles the underlying explanatory factors of variation. However, it remains an open question what kind of training framework could potentially achieve that. Whereas most…

In an independence model, the triplets that represent conditional independences between singletons are called elementary. It is known that the elementary triplets represent the independence model unambiguously under some conditions. In this…

Independence and Conditional Independence (CI) are two fundamental concepts in probability and statistics, which can be applied to solve many central problems of statistical inference. There are many existing independence and CI measures…

Causal additive models provide a tractable yet expressive framework for causal discovery in the presence of hidden variables. When unobserved backdoor or causal paths exist between two variables, their causal relationship is often…

Conditional independence provides a way to understand causal relationships among the variables of interest. An underlying system may exhibit more fine-grained causal relationships especially between a variable and its parents, which will be…

Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly…