Bayesian nonparametric course - Master MASH 2018
Objectives
The course aims at providing a modern overview of Bayesian nonparametric statistics. Students will learn how to model statistical and machine learning problems with Bayesian nonparametric tools and study theoretical properties of the involved objects.
Syllabus
This course covers the fundamentals of Bayesian nonparametric inference and focuses on the key probabilistic concepts and stochastic modelling tools at the basis of the most recent advances in the field.
• Foundations of Bayesian nonparametric inference: exchangeability, de Finetti's representation theorem
• Clustering and Dirichlet process, random partitions
• Models beyond the Dirichlet process, random measures
• Latent features and the Indian buffet process
• Some other popular models: Mixture models, Hierarchical models, Covariate-dependent models, Network models
• Discovery probabilities: comparing BNP & Good-Turing estimators
• Posterior distributions and some elements of Bayesian asymptotics
Mini Seminar
The students will present a paper during the last session (in March). Presentations will be about 20 minutes long. Papers can be chosen in one of the following ways:
- in this list of Bayes deep learning related papers
- in the webpage Tutorials on Bayesian Nonparametrics, maintained by Peter Orbanz, which references some seminal Bayesian nonparametric papers
- by browsing https://scholar.google.fr/ or http://arxiv.org/ with keywords you are interested in
In the last two cases, please send me an email with the reference for approval.
In any case, please fill in the following pad with your name and the reference of the paper.
Lecture notes
Lecture notes (handwritten) essentially based on the following bibliography.
Bibliography
- Jayanta Ghosh, and R. V. Ramamoorthi. 2003. Bayesian Nonparametrics. Springer Series in Statistics.
- Nils Hjort, Chris Holmes, Peter Müller, and Stephen Walker. 2010. Bayesian Nonparametrics. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press.
- Peter Orbanz. 2012. Lecture Notes on Bayesian Nonparametrics. Available at: http://stat.columbia.edu/~porbanz/papers/porbanz_BNP_draft.pdf
- Bas Kleijn, Aad van der Vaart, Harry van Zanten. 2012. Lectures on Nonparametric Bayesian Statistics. Available at: https://staff.fnwi.uva.nl/b.j.k.kleijn/NPBayes-LecNotes-2015.pdf
Who?
Master MASH students.
When?
Further links
Tutorials on Bayesian Nonparametrics, a webpage maintained by Peter Orbanz
DPpackage: Bayesian Semi- and Nonparametric Modeling in R, an R package by Alejandro Jara
BNPdensity, an R package for modeling mixtures with normalized random measures, by Ernesto Barrios, Antonio Lijoi, Luis E. Nieto-Barajas and Igor Prünster