Related papers: No eleventh conditional Ingleton inequality
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…
We study constrained versions of the Ingleton inequality in the entropic setting and quantify its stability under small violations of conditional independence. Although the classical Ingleton inequality fails for general entropy profiles,…
The Ingleton inequality is a classical linear information inequality that holds for representable matroids but fails to be universally valid for entropic vectors. Understanding the extent to which this inequality can be violated has been a…
We consider the problem of conditional independence testing of $X$ and $Y$ given $Z$ where $X,Y$ and $Z$ are three real random variables and $Z$ is continuous. We focus on two main cases - when $X$ and $Y$ are both discrete, and when $X$…
We study the problem of testing \emph{conditional independence} for discrete distributions. Specifically, given samples from a discrete random variable $(X, Y, Z)$ on domain $[\ell_1]\times[\ell_2] \times [n]$, we want to distinguish, with…
Structural independence is the (conditional) independence that arises from the structure rather than the precise numerical values of a distribution. We develop this concept and relate it to $d$-separation and structural causal models.…
Investigation of the reversibility of the directional hierarchy in the interdependency among the notions of conditional independence, conditional mean independence, and zero conditional covariance, for two random variables X and Y given a…
``Behind every limit theorem, there is an inequality'' said Kolmogorov. We say ``for every inequality, there is an approximate inequality under approximate regularity conditions.'' Suppose $X, X'$ are independent and identically distributed…
The method of imsets, introduced by Studen\'y, provides a geometric and combinatorial description of conditional independence statements. Elementary conditional independence statements over a finite set of discrete random variables…
We introduce a test for the conditional independence of random variables $X$ and $Y$ given a random variable $Z$, specifically by sampling from the joint distribution $(X,Y,Z)$, binning the support of the distribution of $Z$, and conducting…
We propose a general new method, the conditional permutation test, for testing the conditional independence of variables $X$ and $Y$ given a potentially high-dimensional random vector $Z$ that may contain confounding factors. The proposed…
In 1997, Z.Zhang and R.W.Yeung found the first example of a conditional information inequality in four variables that is not "Shannon-type". This linear inequality for entropies is called conditional (or constraint) since it holds only…
In this paper, the maximal nonlinear conditional correlation of two random vectors $X$ and $Y$ given another random vector $Z$, denoted by $\rho_1(X,Y|Z)$, is defined as a measure of conditional association, which satisfies certain…
We study properties of two resampling scenarios: Conditional Randomisation and Conditional Permutation schemes, which are relevant for testing conditional independence of discrete random variables $X$ and $Y$ given a random variable $Z$.…
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…
This work investigates the intersection property of conditional independence. It states that for random variables $A,B,C$ and $X$ we have that $X$ independent of $A$ given $B,C$ and $X$ independent of $B$ given $A,C$ implies $X$ independent…
As a crucial problem in statistics is to decide whether additional variables are needed in a regression model. We propose a new multivariate test to investigate the conditional mean independence of Y given X conditioning on some known…
In this paper, we prove a conditional limit theorem for independent not necessarily identically distributed random variables. Namely, we obtain the asymptotic distribution of a large number of them given the sum.
We propose a new method to test conditional independence of two real random variables $Y$ and $Z$ conditionally on an arbitrary third random variable $X$. %with $F_{.|.}$ representing conditional distribution functions, The partial copula…
We propose a test of the conditional independence of random variables $X$ and~$Y$ given~$Z$ under the additional assumption that $X$ is stochastically nondecreasing in~$Z$. The well-documented hardness of testing conditional independence…