Thematic Axis:
Uncertainty Representation & Quantification

Leader(s)

Arthur Hoarau Frédéric Pennerath

Description

Whether it concerns trust, performance, or transparency, the Representation and Quantification of Uncertainty is at the forefront of Machine Learning and Deep Learning research. The ability for a model to genuinely say I don’t know, to learn from fewer data points or in record time, to provide predictions in critical domains with strict or frequentist guarantees, and to make its reasoning more transparent: these form the core objectives and challenges of this research axis.

Uncertainty Quantification

Uncertainty quantification addresses the magnitude (how much) of a model’s uncertainty. In other words, it assigns a numerical value to quantify that uncertainty. For instance, in a predictive maintenance pipeline assisted by AI, a model might output a score of 0.7 to indicate that a machine is about to fail. In a classification task, a model might hesitate between two classes, Bird and Airplane, assigning each a probability of 0.5. Or, in a medical setting, a model might predict that a new COVID-19 patient lies 0.7 away from the classes it was trained on (such as the flue), supporting the need for human investigation.

Uncertainty Representation

Uncertainty representation addresses the nature (how) of uncertainty. Saying I don’t know because a coin has a 50% chance of landing heads is fundamentally different from saying I don’t know because one is unsure whether the coin is fair. The goal here is therefore to establish a principled framework for uncertainty quantification, to theorize the practice. For example, probability theory is well-suited for representing frequentist stochastic phenomena, but it reaches its limits when it comes to representing complete ignorance. The Theory of Belief Functions can provide a suitable framework in discrete settings. Fuzzy sets, in turn, offer a way to handle the non-disjointness of events, for instance, when the temperature is lukewarm rather than strictly cold or hot, or when the weather is cloudy rather than simply sunny or rainy.

Topics

Epistemic Uncertainty Quantification in Machine Learning

A key challenge in machine learning is for a model to be able to genuinely say I don’t know. Recent advances in Machine Learning and Deep Learning have shown that this is far from trivial, and many practical observations reveal counter-intuitive or even undesirable results. Numerous challenges have yet to be addressed.

Members of interest

Arthur Hoarau, Frédéric Pennerath, Brieuc Conan-Guez

Uncertainty-driven Machine Learning

While other research topics treat uncertainty quantification as an end in itself, it can also serve as a tool for a range of other tasks. For example, it can augment supervised learning with a rejection option, allowing a model to abstain when a problem is too difficult or when training data is insufficient. It can also help reduce the ecological, societal, and economic costs of labelling, by selecting only a subset of instances to annotate, focusing on regions of interest in the input space. Theoretical bounds can furthermore be derived to provide reliability guarantees on the model’s predictions.

Members of interest

Arthur Hoarau, Frédéric Pennerath, Brieuc Conan-Guez, Lydia Boudjeloud-Assala, Fabien Lauer, Mathieu d’Aquin, Chahrazed Labba

Representations of Uncertainty

Representing uncertainty and imprecision is not straightforward. Beyond that Machine Learning and Deep Learning architectures tend to rely on classical probability theory, a number of alternatives are worth considering. We therefore also investigate alternative frameworks, such as possibility theory, credal sets, belief function theory, fuzzy sets, and subjective logic.

Members of interest

Arthur Hoarau, Jean Lieber, Armelle Brun, Mathieu d’Aquin

Recent Projects

OPTIMUS-Prime

In this project, we proposed heatmaps highlighting the image regions that support the model’s prediction. Beyond making the model’s decision more transparent, these heatmaps are theoretically grounded in concepts extracted by the deep classifier: minimal and sufficient to guarantee the model’s prediction.

Evidential Deep Learning is not Evidential Learning

Several families of methods exist to enable a model to say I don’t know, but none has reached consensus and some have recently faced sharp criticism. Here we show that one particular family of methods satisfies a key axiom: the model’s ignorance decreases as the training set grows larger. The model’s error is reported on CIFAR-10 and MNIST, surrounded by an interval representing its ignorance: the larger the training set, the less ignorant the model.

Seminars

• Vitor Martin Bordini (UTC, Heudiasyc) — Cautious Self-Learning via Labelwise Uncertainty Quantification
• Louenas Bounia (LIPN, Paris-Nord) — Modèles formels pour l’IA explicable : des explications pour les arbres
• Arthur Hoarau (Loria, CentraleSupélec) — Uncertainty quantification with classification models for better explainability and human-in-the-Loop systems

Ongoing & Related Projetcs

Masters

• Youness BAHADDOU — Détection d’anomalies ou d’incohérences locales dans des images en apprentissage automatique profond

Thesis

• Mathias COURAUD — Design and deployment of an intelligent decision support system for the sustainable management of green dependencies: Towards the integration of heterogeneous data and the development of eco-responsible maintenance strategies
• Rania AIT CHABANE — Conception et mise en œoeuvre d’un système d’Adaptive Learning Explicable basé sur des graphes de connaissance et de l’apprentissage fédéré

Publications

2026

1. Can we trust our models? Epistemic calibration in second-order classification. Pre-Print 2026. Arthur Hoarau.

2. OPTIMUS-Prime: Minimal & Sufficient Concept Explanations for Deep Vision Models. Pre-Print 2026. Arthur Hoarau, Chenrui Zhu, Vu-Linh Nguyen.

3. Et si les classifieurs profonds oubliaient l’inconnu ? Auto-encodeurs et détection hors distribution. CNIA-PFIA 2026. François Thievon, Arthur Hoarau.

4. Uncertainty-Aware Knowledge Tracing: Towards the Use of Subjective Logic Workshop Explainable AI in Education at Learning Analytics and Knowledge 2026. Rania Ait Chabane, Armelle Brun, Azim Roussanaly.

5. A New Domain-Informed Learner Model with Uncertainty-Aware Knowledge Mastery Propagation Educational Data Mining 2026. Rania Ait Chabane, Armelle Brun, Azim Roussanaly.

6. Uniform Error Bounds for Quantized Dynamical Models. IFAC Journal of Systems and Control 2026. Abdelkader Metakalard, Fabien Lauer, Kevin Colin, Marion Gilson.

7. Evidential Deep Learning is not Evidential Learning: A Clear Distinction. Advances in Intelligent Data Analysis 2026. Arthur Hoarau.

8. Reducing Aleatoric and Epistemic Uncertainty through Multi-modal Data Acquisition. Machine Learning Journal, ECML-PKDD 2026. Arthur Hoarau, Benjamin Quost, Sébastien Destercke, Willem Waegeman.