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

arXiv: https://arxiv.org/abs/2208.09344 · HTML: https://mlsanity.com/paper/2208.09344/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 42 references that are in the map.
- First posted on arXiv 19 Aug 2022.

## Builds on (most cited first, 7 of 7)

- [Estimation of positive definite M-matrices and structure learning for attractive Gaussian Markov Random fields](https://mlsanity.com/paper/1404.6640/) (2014)
- [Maximum likelihood estimation in Gaussian models under total positivity](https://mlsanity.com/paper/1702.04031/) (2017)
- [Learning High-dimensional Gaussian Graphical Models under Total Positivity without Adjustment of Tuning Parameters](https://mlsanity.com/paper/1906.05159/) (2019)
- [Pivotal Pruning of Trade-offs in QPNs](https://mlsanity.com/paper/1301.3889/) (2013)
- [Enhancing QPNs for Trade-off Resolution](https://mlsanity.com/paper/1301.6735/) (2013)
- [Refining Reasoning in Qualitative Probabilistic Networks](https://mlsanity.com/paper/1302.4975/) (2013)
- [Intercausal Reasoning with Uninstantiated Ancestor Nodes](https://mlsanity.com/paper/1303.1492/) (2013)

## Abstract (arXiv)

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.