Description du projet
Faire la lumière sur la boîte noire des algorithmes bayésiens pour les mégadonnées
L’analyse bayésienne, une méthode d’inférence statistique qui applique les probabilités pour actualiser notre croyance sur le modèle en fonction des observations, est fondamentale pour de nombreux algorithmes statistiques et d’apprentissage automatique dédiés aux mégadonnées. Elle favorise la compréhension des processus dans le cadre de problèmes complexes, notamment l’évaluation du changement climatique et le suivi de la propagation d’une maladie. Cependant, les méthodes bayésiennes atteignent leurs limites face à l’explosion des données disponibles, et les tentatives d’accélération du traitement sont en grande partie des solutions de type «boîte noire». Le projet BigBayesUQ, financé par l’UE, développe une théorie pour les méthodes bayésiennes évolutives qui permet de quantifier les performances, les limites et l’incertitude. Ceci améliorera la précision et le soutien ultérieur d’une large communauté de scientifiques et de chercheurs.
Objectif
Recent years have seen a rapid increase in available information. This has created an urgent need for fast statistical and machine learning methods that can scale up to big data sets. Standard approaches, including the now routinely used Bayesian methods, are becoming computationally infeasible, especially in complex models with many parameters and large data sizes. A variety of algorithms have been proposed to speed up these procedures, but these are typically black box methods with very limited theoretical support. In fact empirical evidence shows the potentially bad performance of such methods. This is especially concerning in real-world applications, e.g. in medicine. In this project I shall open up the black box and provide a theory for scalable Bayesian methods combining recent, state-of-the-art techniques from Bayesian nonparametrics, empirical process theory, and machine learning. I focus on two very important classes of scalable techniques: variational and distributed Bayes. I shall establish guarantees, but also limitations, of these procedures for estimating the parameter of interest, and for quantifying the corresponding uncertainty, within a framework that will also convince outside of the Bayesian paradigm. As a result, scalable Bayesian techniques will have more accurate performance, and also better acceptance by a wider community of scientists and practitioners. The proposed research, although motivated by real world problems, is of a mathematical nature. In the analysis I consider mathematical models, which are routinely used in various fields (e.g. high-dimensional linear and logistic regressions are the work horses in econometrics or genetics). My theoretical results will provide principled new insights that can be used, for instance in multiple specific applications I am involved in, including developing novel statistical methods for understanding fundamental questions in cosmology and the early detection of dementia using multiple data sources.
Champ scientifique
- natural sciencescomputer and information sciencesdata sciencebig data
- natural sciencesmathematicsapplied mathematicsstatistics and probabilitybayesian statistics
- natural sciencescomputer and information sciencesartificial intelligencemachine learning
- natural sciencesmathematicsapplied mathematicsmathematical model
Programme(s)
- HORIZON.1.1 - European Research Council (ERC) Main Programme
Thème(s)
Régime de financement
HORIZON-AG - HORIZON Action Grant Budget-BasedInstitution d’accueil
20136 Milano
Italie