Conditional independence of blocked ordered data

Propositional Independence Conditional independence

Independence – the study of what is relevant to a given problem of reasoning – is an important AI topic. In this paper, we investigate several notions of conditional independence in propositional logic: Darwiche and Pearl’s conditional independence, and two more restricted forms of it, called strong conditional independence and perfect conditional independence. Many characterizations and proper...

Nonparametric analysis of blocked ordered categories data: some examples revisited

In this paper, we will use Cochran-Mantel-Haenszel (CMH) statistics to analyse four data sets which have appeared in the literature. It is well known that tests based on the CMH statistics are equivalent to certain standard rank tests but here we show how CMH statistics also apply in less standard situations. In particular, examples are given for randomized block designs both with and without m...

Towards Conditional Independence Test for Relational Data

Conditional independence (CI) tests play a central role in statistical inference, machine learning, and causal discovery. Most existing CI tests assume that the samples are independently and identically distributed (i.i.d.). However, this assumption often does not hold in the case of relational data. We define Relational Conditional Independence (RCI), a generalization of CI to the relational s...

Conditional Independence

Conditional independence, conditional mixing and conditional association

Some properties of conditionally independent random variables are studied. Conditional versions of generalized Borel-Cantelli lemma, generalized Kolmogorov’s inequality and generalized Hájek-Rényi inequality are proved. As applications, a conditional version of the strong law of large numbers for conditionally independent random variables and a conditional version of the Kolmogorov’s strong law...