# A geometric approach to conditioning belief functions

arXiv: https://arxiv.org/abs/2104.10651 · HTML: https://mlsanity.com/paper/2104.10651/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 145 references that are in the map.
- First posted on arXiv 21 Apr 2021.

## Builds on (most cited first, 9 of 9)

- [Image Segmentation Using Deep Learning: A Survey](https://mlsanity.com/paper/2001.05566/) (2020)
- [Decision-Making with Belief Functions: a Review](https://mlsanity.com/paper/1808.05322/) (2018)
- [Visions of a generalized probability theory](https://mlsanity.com/paper/1810.10341/) (2018)
- [Decision under Uncertainty](https://mlsanity.com/paper/1304.1527/) (2013)
- [Expert Opinion Extraction from a Biomedical Database](https://mlsanity.com/paper/1709.03270/) (2017)
- [The Dynamic of Belief in the Transferable Belief Model and Specialization-Generalization Matrices](https://mlsanity.com/paper/1303.5408/) (2013)
- [A New Approach to Updating Beliefs](https://mlsanity.com/paper/1304.1119/) (2013)
- [Faithful Approximations of Belief Functions](https://mlsanity.com/paper/1301.6703/) (2013)
- [Jeffrey's rule of conditioning generalized to belief functions](https://mlsanity.com/paper/1303.1514/) (2013)

## Abstract (arXiv)

Conditioning is crucial in applied science when inference involving time series is involved. Belief calculus is an effective way of handling such inference in the presence of epistemic uncertainty -- unfortunately, different approaches to conditioning in the belief function framework have been proposed in the past, leaving the matter somewhat unsettled. Inspired by the geometric approach to uncertainty, in this paper we propose an approach to the conditioning of belief functions based on geometrically projecting them onto the simplex associated with the conditioning event in the space of all belief functions. We show here that such a geometric approach to conditioning often produces simple results with straightforward interpretations in terms of degrees of belief. This raises the question of whether classical approaches, such as for instance Dempster's conditioning, can also be reduced to some form of distance minimisation in a suitable space. The study of families of combination rules generated by (geometric) conditioning rules appears to be the natural prosecution of the presented research.