# Credal Prediction based on Relative Likelihood

arXiv: https://arxiv.org/abs/2505.22332 · HTML: https://mlsanity.com/paper/2505.22332/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 63 references that are in the map.
- First posted on arXiv 28 May 2025.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Human uncertainty makes classification more robust](https://mlsanity.com/paper/1908.07086/) (2019)
- [What Can We Learn from Collective Human Opinions on Natural Language Inference Data?](https://mlsanity.com/paper/2010.03532/) (2020)
- [Hyperparameter Ensembles for Robustness and Uncertainty Quantification](https://mlsanity.com/paper/2006.13570/) (2020)
- [Repulsive Deep Ensembles are Bayesian](https://mlsanity.com/paper/2106.11642/) (2021)
- [On the Existence of Simpler Machine Learning Models](https://mlsanity.com/paper/1908.01755/) (2019)
- [A Unified Theory of Diversity in Ensemble Learning](https://mlsanity.com/paper/2301.03962/) (2023)
- [No One Representation to Rule Them All: Overlapping Features of Training Methods](https://mlsanity.com/paper/2110.12899/) (2021)
- [Is one annotation enough? A data-centric image classification benchmark for noisy and ambiguous label estimation](https://mlsanity.com/paper/2207.06214/) (2022)
- [Conformalized Credal Set Predictors](https://mlsanity.com/paper/2402.10723/) (2024)
- [Rashomon Sets for Prototypical-Part Networks: Editing Interpretable Models in Real-Time](https://mlsanity.com/paper/2503.01087/) (2025)
- [Deep Anti-Regularized Ensembles provide reliable out-of-distribution uncertainty quantification](https://mlsanity.com/paper/2304.04042/) (2023)
- [Credal Model Averaging for classification: representing prior ignorance and expert opinions](https://mlsanity.com/paper/1405.3559/) (2014)

## Built on by (most cited first, 8 of 8)

- [Learning Credal Ensembles via Distributionally Robust Optimization](https://mlsanity.com/paper/2602.08470/) (2026)
- [Quantification of Credal Uncertainty: A Distance-Based Approach](https://mlsanity.com/paper/2603.27270/) (2026)
- [Maxitive Donsker-Varadhan Formulation for Possibilistic Variational Inference](https://mlsanity.com/paper/2511.21223/) (2025)
- [Set-based v.s. Distribution-based Representations of Epistemic Uncertainty: A Comparative Study](https://mlsanity.com/paper/2602.22747/) (2026)
- [Efficient Credal Prediction through Decalibration](https://mlsanity.com/paper/2603.08495/) (2026)
- [Structured Credal Learning](https://mlsanity.com/paper/2603.14070/) (2026)
- [Upper Entropy for 2-Monotone Lower Probabilities](https://mlsanity.com/paper/2603.23558/) (2026)
- [Possibilistic Predictive Uncertainty for Deep Learning](https://mlsanity.com/paper/2605.00600/) (2026)

## Abstract (arXiv)

Predictions in the form of sets of probability distributions, so-called credal sets, provide a suitable means to represent a learner's epistemic uncertainty. In this paper, we propose a theoretically grounded approach to credal prediction based on the statistical notion of relative likelihood: The target of prediction is the set of all (conditional) probability distributions produced by the collection of plausible models, namely those models whose relative likelihood exceeds a specified threshold. This threshold has an intuitive interpretation and allows for controlling the trade-off between correctness and precision of credal predictions. We tackle the problem of approximating credal sets defined in this way by means of suitably modified ensemble learning techniques. To validate our approach, we illustrate its effectiveness by experiments on benchmark datasets demonstrating superior uncertainty representation without compromising predictive performance. We also compare our method against several state-of-the-art baselines in credal prediction.