Bayesian machine learning

ECTS : 4

Volume horaire : 24

Description du contenu de l'enseignement :

Bayesian Nonparametrics:

• Introduction
• The Dirichlet Process
• Infinite Mixture models
• Posterior Sampling
• Models beyond the Dirichlet Process
• Gaussian Processes
• Selected applications

Bayesian Deep Learning

• Why do we want parameter uncertainty
• Priors for Bayesian neural networks
• Posterior inference
• Martingale Posteriors and generalised Bayesian Inference

Compétence à acquérir :

Essentials of Bayesian Nonparametrics, main concepts for Bayesian Deep Learning

Mode de contrôle des connaissances :

Final exam and homework

Bibliographie, lectures recommandées :

• Hjort NL, Holmes C, Müller P, Walker SG, editors. Bayesian nonparametrics. Cambridge University Press; 2010 Apr 12.
• Ghosal S, Van der Vaart AW. Fundamentals of nonparametric Bayesian inference. Cambridge University Press; 2017 Jun 26.
• Williams CK, Rasmussen CE. Gaussian processes for machine learning. Cambridge, MA: MIT press; 2006.
• Many references at https://www.gatsby.ucl.ac.uk/~porbanz/npb-tutorial.html
• Murphy KP. Probabilistic machine learning: Advanced topics. MIT press; 2023 Aug 15.
• Fong E, Holmes C, Walker SG. Martingale posterior distributions. Journal  of the Royal Statistical Society Series B: Statistical Methodology.  2023 Nov;85(5):1357-91.