Related papers: Conditional Independence Beyond Domain Separabilit…
On 12 February 2020 the Royal Statistical Society hosted a meeting to discuss the forthcoming paper ``Graphical models for extremes'' by Sebastian Engelke and Adrien Hitz [arXiv:1812.01734]. This short note is a supplement to my discussion…
Conditional independence and graphical models are well studied for probability distributions on product spaces. We propose a new notion of conditional independence for any measure $\Lambda$ on the punctured Euclidean space $\mathbb…
This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional…
Recently, Forr\'e (arXiv:2104.11547, 2021) introduced transitional conditional independence, a notion of conditional independence that provides a unified framework for both random and non-stochastic variables. The original paper establishes…
In this article we provide a substantial discussion on the statistical concept of conditional independence, which is not routinely mentioned in most elementary statistics and mathematical statistics textbooks. Under the assumption of…
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…
We study extremal conditional independence for H\"{u}sler-Reiss distributions, which is a parametric subclass of multivariate Pareto distributions. As the main contribution, we introduce two set functions, i.e.~functions which assign a…
We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of…
Conditioned limit laws constitute an important and well developed framework of extreme value theory that describe a broad range of extremal dependence forms including asymptotic independence. We explore the assumption of conditional…
Conditional independence, graphical models and sparsity are key notions for parsimonious statistical models and for understanding the structural relationships in the data. The theory of multivariate and spatial extremes describes the risk…
We introduce a nonparametric graphical model for discrete node variables based on additive conditional independence. Additive conditional independence is a three way statistical relation that shares similar properties with conditional…
The goal of this paper is to integrate the notions of stochastic conditional independence and variation conditional independence under a more general notion of extended conditional independence. We show that under appropriate assumptions…
In this work we handle with categorical (ordinal) variables and we focus on the (in)dependence relationship under the marginal, conditional and context-specific perspective. If the first two are well known, the last one concerns…
Conditional independence is a crucial concept supporting adequate modelling and efficient reasoning in probabilistics. In knowledge representation, the idea of conditional independence has also been introduced for specific formalisms, such…
We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely…
Multivariate extreme value analysis quantifies the probability and magnitude of joint extreme events. River discharges from the upper Danube River basin provide a challenging dataset for such analysis because the data, which is measured on…
Graphical models are a key class of probabilistic models for studying the conditional independence structure of a set of random variables. Circular variables are special variables, characterized by periodicity, arising in several contexts…
We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data…
This article proposes a generalized notion of extreme multivariate dependence between two random vectors which relies on the extremality of the cross-covariance matrix between these two vectors. Using a partial ordering on the…
Conditional independence plays a foundational role in database theory, probability theory, information theory, and graphical models. In databases, conditional independence appears in database normalization and is known as the (embedded)…