Intercausal Reasoning with Uninstantiated Ancestor Nodes

TL;DR

This paper introduces a new definition of product synergy for intercausal reasoning that accounts for uninstantiated ancestor nodes, ensuring more accurate probabilistic inference in complex Bayesian networks.

Contribution

It proposes a novel concept of half positive semi-definiteness to improve the understanding of intercausal dependence with unobserved causes.

Findings

New definition of product synergy for uninstantiated causes

Proves adequacy of the new definition for direct and indirect evidence

Introduces the concept of half positive semi-definiteness

Abstract

Intercausal reasoning is a common inference pattern involving probabilistic dependence of causes of an observed common effect. The sign of this dependence is captured by a qualitative property called product synergy. The current definition of product synergy is insufficient for intercausal reasoning where there are additional uninstantiated causes of the common effect. We propose a new definition of product synergy and prove its adequacy for intercausal reasoning with direct and indirect evidence for the common effect. The new definition is based on a new property matrix half positive semi-definiteness, a weakened form of matrix positive semi-definiteness.