Bayesian nonparametric statistics

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

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?

The course is intended for PhD students of MSTII Ecole doctorale. However, it is open to anyone interested.

When?

On Thursday mornings, 9.00 to 12.00, January 5, 12, 19, 26 and February 2, 2017

GoogleCal iCal format, html format

Where?

Room A103, Inria Grenoble Rhône-Alpes

655 Avenue de l'Europe

38330 Montbonnot-Saint-Martin

How do I register?

Send me an email: julyan.arbel@inria.fr

Further links

Tutorials and Videolectures

Books and Chapters

Upcoming 11th Conference on Bayesian Nonparametrics. Paris, 26-30 June 2017

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