"Conditional Inter-Causally Independent" Node Distributions, a Property of "Noisy-Or" Models

TL;DR

This paper explores the conditions under which noisy-or models exhibit inter-causal independence, revealing new semantics for noisy-or as a measure of conflict among hypotheses sharing evidence.

Contribution

It demonstrates that inter-causal independence can occur in noisy-or models at specific evidence states, linking two measures of inter-causal effect and providing new interpretative semantics.

Findings

Inter-causal independence is possible at certain evidence states.

Multiplicative and additive synergies are equal in CICI distributions.

Noisy-or models can be interpreted as conflict measures among hypotheses.

Abstract

This paper examines the interdependence generated between two parent nodes with a common instantiated child node, such as two hypotheses sharing common evidence. The relation so generated has been termed "intercausal." It is shown by construction that inter-causal independence is possible for binary distributions at one state of evidence. For such "CICI" distributions, the two measures of inter-causal effect, "multiplicative synergy" and "additive synergy" are equal. The well known "noisy-or" model is an example of such a distribution. This introduces novel semantics for the noisy-or, as a model of the degree of conflict among competing hypotheses of a common observation.