Nash Conditional Independence Curve

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...

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...

Independence and Conditional Independence in Causal Systems

This paper studies the interrelations between independence or conditional independence and causal relations, defined in terms of functional dependence, that hold among variables of interest within the settable system framework of White and Chalak. We provide formal conditions ensuring the validity of Reichenbach’s principle of common cause and introduce a new conditional counterpart, the condit...

Probabilistic Conditional Independence Structuresand

1 Franti sek Mat u s Prague ABSTRACT. Special conditional independence structures have been recognized to be matroids. This opens new possibilities for the application of matroid theory methods (duality, minors, expansions) to the study of conditional independence and, on the other hand, starts a new probabilistic branch of matroid representation theory. 2