Intercausal Reasoning with Uninstantiated Ancestor Nodes
This work addresses a limitation in probabilistic inference for AI and statistics, but it appears incremental as it refines an existing concept.
The paper tackled the problem of intercausal reasoning with uninstantiated ancestor nodes by proposing a new definition of product synergy, proving its adequacy for handling direct and indirect evidence.
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.