[2603.04204] Beyond Mixtures and Products for Ensemble Aggregation: A Likelihood Perspective on Generalized Means

Statistics > Machine Learning arXiv:2603.04204 (stat) [Submitted on 4 Mar 2026] Title:Beyond Mixtures and Products for Ensemble Aggregation: A Likelihood Perspective on Generalized Means Authors:Raphaël Razafindralambo, Rémy Sun, Frédéric Precioso, Damien Garreau, Pierre-Alexandre Mattei View a PDF of the paper titled Beyond Mixtures and Products for Ensemble Aggregation: A Likelihood Perspective on Generalized Means, by Rapha\"el Razafindralambo and 4 other authors View PDF HTML (experimental) Abstract:Density aggregation is a central problem in machine learning, for instance when combining predictions from a Deep Ensemble. The choice of aggregation remains an open question with two commonly proposed approaches being linear pooling (probability averaging) and geometric pooling (logit averaging). In this work, we address this question by studying the normalized generalized mean of order $r \in \mathbb{R} \cup \{-\infty,+\infty\}$ through the lens of log-likelihood, the standard evaluation criterion in machine learning. This provides a unifying aggregation formalism and shows different optimal configurations for different situations. We show that the regime $r \in [0,1]$ is the only range ensuring systematic improvements relative to individual distributions, thereby providing a principled justification for the reliability and widespread practical use of linear ($r=1$) and geometric ($r=0$) pooling. In contrast, we show that aggregation rules with $r \notin [0,1]$ may fail t...