Related papers: Conditional Independence in Possibility Theory

Conditional independence, and more generally conditional mutual independence, are central notions in probability theory. In their general forms, they include functional dependence as a special case. In this paper, we tackle two fundamental…

Conditional independence and Markov properties are powerful tools allowing expression of multidimensional probability distributions by means of low-dimensional ones. As multidimensional possibilistic models have been studied for several…

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…

An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability…

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…

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…

In this paper we investigate the notion of conditional independence and prove several information inequalities for conditionally independent random variables.

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…

Independence and conditional independence are fundamental concepts for reasoning about groups of random variables in probabilistic programs. Verification methods for independence are still nascent, and existing methods cannot handle…

Conditional independence testing is a key problem required by many machine learning and statistics tools. In particular, it is one way of evaluating the usefulness of some features on a supervised prediction problem. We propose a novel…

Two known results on the relationship between conditional and unconditional independence are obtained as a consequence of the main result of this paper, a theorem that uses independence of Markov kernels to obtain a minimal condition which…

Measuring conditional dependencies among the variables of a network is of great interest to many disciplines. This paper studies some shortcomings of the existing dependency measures in detecting direct causal influences or their lack of…

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…

Starting from elementary considerations about independence and Markov processes in classical probability we arrive at the new concept of conditional monotone independence (or operator-valued monotone independence). With the help of product…

This paper studies the connection between probabilistic conditional independence in uncertain reasoning and data dependency in relational databases. As a demonstration of the usefulness of this preliminary investigation, an alternate proof…

In this paper we provide a theoretical analysis of counterfactual invariance. We present a variety of existing definitions, study how they relate to each other and what their graphical implications are. We then turn to the current major…

This paper introduces the notions of independence and conditional independence in valuation-based systems (VBS). VBS is an axiomatic framework capable of representing many different uncertainty calculi. We define independence and…

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.…

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…

Testing conditional independence has many applications, such as in Bayesian network learning and causal discovery. Different test methods have been proposed. However, existing methods generally can not work when only discretized…