# Reasoning with random sets: An agenda for the future

arXiv: https://arxiv.org/abs/2401.09435 · HTML: https://mlsanity.com/paper/2401.09435/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 210 references that are in the map.
- First posted on arXiv 19 Dec 2023.

## Builds on (most cited first, 10 of 10)

- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Deep Transfer Learning with Joint Adaptation Networks](https://mlsanity.com/paper/1605.06636/) (2016)
- [Random-Set Neural Networks (RS-NN)](https://mlsanity.com/paper/2307.05772/) (2023)
- [Epistemic Deep Learning](https://mlsanity.com/paper/2206.07609/) (2022)
- [Visions of a generalized probability theory](https://mlsanity.com/paper/1810.10341/) (2018)
- [Distributionally Robust Statistical Verification with Imprecise Neural Networks](https://mlsanity.com/paper/2308.14815/) (2023)
- [Uncertainty measures: The big picture](https://mlsanity.com/paper/2104.06839/) (2021)
- [A New Approach to Updating Beliefs](https://mlsanity.com/paper/1304.1119/) (2013)
- [An introduction to optimization under uncertainty -- A short survey](https://mlsanity.com/paper/2212.00862/) (2022)

## Built on by (most cited first, 6 of 6)

- [Random-Set Large Language Models](https://mlsanity.com/paper/2504.18085/) (2025)
- [Epistemic Generative Adversarial Networks](https://mlsanity.com/paper/2603.18348/) (2026)
- [Random-Set Graph Neural Networks](https://mlsanity.com/paper/2605.11987/) (2026)
- [Statistical inference with belief functions: A survey](https://mlsanity.com/paper/2605.07908/) (2026)
- [A neurosymbolic Approach with Epistemic Deep Learning for Hierarchical Image Classification](https://mlsanity.com/paper/2605.16383/) (2026)
- [XU-RS: Explaining Credal Width in Random-Set Language Models](https://mlsanity.com/paper/2609.37594/) (2026)

## Abstract (arXiv)

In this paper, we discuss a potential agenda for future work in the theory of random sets and belief functions, touching upon a number of focal issues: the development of a fully-fledged theory of statistical reasoning with random sets, including the generalisation of logistic regression and of the classical laws of probability; the further development of the geometric approach to uncertainty, to include general random sets, a wider range of uncertainty measures and alternative geometric representations; the application of this new theory to high-impact areas such as climate change, machine learning and statistical learning theory.