Category-theoretic Structure for Independence and Conditional Independence

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...

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...

Conditional Independence

The Assumption of Class-conditional Independence in Category Learning

This paper investigates the role of the assumption of classconditional independence of object features in human classification learning. This assumption holds that object feature values are statistically independent of each other, given knowledge of the object’s true category. Treating features as classconditionally independent can in many situations substantially facilitate learning and catego...

Girth, minimum degree, independence, and broadcast independence

An independent broadcast on a connected graph $G$is a function $f:V(G)to mathbb{N}_0$such that, for every vertex $x$ of $G$, the value $f(x)$ is at most the eccentricity of $x$ in $G$,and $f(x)>0$ implies that $f(y)=0$ for every vertex $y$ of $G$ within distance at most $f(x)$ from $x$.The broadcast independence number $alpha_b(G)$ of $G$is the largest weight $sumlimits_{xin V(G)}f(x)$of an ind...