ML-MTP is a series of seminars aiming to federate the Machine Learning community around Montpellier, hosting talks from local researchers as well as national and international experts.
Inria Montpellier, St-Priest Campus, Building 2, Room 167
Paul-Gauthier Noé LIS – CNRS/ Aix Marseille Université
While calibration of probabilistic predictions has been widely studied, we will rather discuss calibration of likelihood functions. This has been studied, especially in biometrics, in cases with only two exhaustive and mutually exclusive hypotheses (or classes): where likelihood functions can be written as log-likelihood-ratios (LLRs). After defining calibration for LLRs and its connection with the concept of weight-of-evidence, I will present the idempotence property and its associated constraint on the distribution of the LLRs. Although these results have been known for decades, they have been limited to the binary case. In this talk, we will see how the Aitchison geometry of the simplex allows us to extend these results to cases with more than two hypotheses. To be more precise, it recovers, in a vector form, the additive form of the Bayes’ rule; extending therefore the LLR and the weight-of-evidence to any number of hypotheses. Especially, we will extend the definition of calibration, the idempotence, and the constraint on the distribution of likelihood functions to this multiple hypotheses and multiclass counterpart of the LLR: the isometric-log-ratio transformed likelihood function. Even if this work is mainly conceptual, we will discuss one application to machine learning by presenting a non-linear discriminant analysis where the discriminant components form a calibrated likelihood function over the classes, improving therefore the interpretability and the reliability of the method.
Inria Montpellier, St-Priest Campus, Building 2, Room 167
Paul-Gauthier Noé LIS – CNRS/ Aix Marseille Université
While calibration of probabilistic predictions has been widely studied, we will rather discuss calibration of likelihood functions. This has been studied, especially in biometrics, in cases with only two exhaustive and mutually exclusive hypotheses (or classes): where likelihood functions can be written as log-likelihood-ratios (LLRs). After defining calibration for LLRs and its connection with the concept of weight-of-evidence, I will present the idempotence property and its associated constraint on the distribution of the LLRs. Although these results have been known for decades, they have been limited to the binary case. In this talk, we will see how the Aitchison geometry of the simplex allows us to extend these results to cases with more than two hypotheses. To be more precise, it recovers, in a vector form, the additive form of the Bayes’ rule; extending therefore the LLR and the weight-of-evidence to any number of hypotheses. Especially, we will extend the definition of calibration, the idempotence, and the constraint on the distribution of likelihood functions to this multiple hypotheses and multiclass counterpart of the LLR: the isometric-log-ratio transformed likelihood function. Even if this work is mainly conceptual, we will discuss one application to machine learning by presenting a non-linear discriminant analysis where the discriminant components form a calibrated likelihood function over the classes, improving therefore the interpretability and the reliability of the method.
Inria Montpellier, St-Priest Campus, Building 5, Room 03.124
Pierre-Alexandre Mattei Inria (Maasai)
Ensemble methods combine predictions from various statistical learning models. Their most famous representatives are random forests or deep ensembles. This talk will center around the question: « How many models should I aggregate? »
We will see that the answer depends on the chosen performance metric. Specifically, in the case of convex losses (such as cross-entropy in classification or mean squared error in regression), the error is a decreasing function of the number of models. In the case of non-convex losses (such as classification error in classification or the Fréchet Inception distance in generative modelling), things are more nuanced, and the error can sometimes be non-monotonic.
These results will be illustrated with examples of neural network ensembles, both for classification and generative modelling. This work is notably based on the papers:
– Are Ensembles Getting Better All the Time? (with Damien Garreau), JMLR 2025
– When Are Two Scores Better Than One? Investigating Ensembles of Diffusion Models (with Raphaël Razafindralambo, Rémy Sun, Frédéric Precioso, and Damien Garreau), TMLR 2026
– Beyond Mixtures and Products for Ensemble Aggregation: A Likelihood Perspective on Generalized Means (with Raphaël Razafindralambo, Rémy Sun, Frédéric Precioso, and Damien Garreau), arXiv 2026
