A note on incorrect inferences in non-binary qualitative probabilistic networks

TL;DR

This paper identifies a fundamental flaw in non-binary qualitative probabilistic networks, showing that many inferences are mathematically incorrect due to an incorrect symmetry property, and discusses potential fixes.

Contribution

It reveals a key incorrect symmetry assumption in non-binary QPNs and highlights the resulting invalid inferences, proposing possible solutions.

Findings

Many inferences in non-binary QPNs are mathematically invalid

Incorrect symmetry property causes inference errors

Discussion of potential resolutions to the problem

Abstract

Qualitative probabilistic networks (QPNs) combine the conditional independence assumptions of Bayesian networks with the qualitative properties of positive and negative dependence. They formalise various intuitive properties of positive dependence to allow inferences over a large network of variables. However, we will demonstrate in this paper that, due to an incorrect symmetry property, many inferences obtained in non-binary QPNs are not mathematically true. We will provide examples of such incorrect inferences and briefly discuss possible resolutions.