CIS 700 - Advanced Topics in ML

CIS 700 - Advanced Topics in Machine Learning - Spring 08
Monte Carlo Methods and Nonparametric Bayesian Models

Instructor: Ben Taskar
Lectures: Towne 303, Monday and Wednesday, 10:30-12:00
Office hours: by appointment

Announcements

First class: Wednesday, January 15.
No class on Monday, January 21 (MLK Jr. Day)
Second class: Wednesday, January 23.

Course description and mechanics

This is an informal seminar-style course on advanced topics in Machine Learning and Probabilistic Reasoning. I will give some lectures on the fundamentals and ask you to present topical papers. We will cover the latest work in Monte Carlo methods and Non-Parametric Bayesian Methods, both theory and applications in computer vision, robotics, natural language understanding, signal processing, computational biology and other fields. Topics include sampling (Gibbs, Importance, Metropolis-Hastings, Slice, Swendsen-Wang, Perfect) and non-parametric models/processes (Dirichlet, Pitman-Yor, Indian-Buffet, etc).

Materials

There is no required textbook for this course. Photocopies of selected chapters from the following books will be handed out in class.

Monte Carlo Statistical Methods (2nd Edition) by Christian P. Robert, George Casella. Springer.
Michael I. Jordan, An Introduction to Probabilistic Graphical Models, in preparation.
Daphne Koller and Nir Friedman, Structured Probabilistic Models, in preparation.

Pre-requisites

CIS 520 or 521. Knowledge of basic probability and statistics, linear algebra, dynamic programming. Exposure to graph theory and algorithms, information theory, optimization will be helpful.

Grading

Participation: 20%.
Short quizzes, attendance, asking and answering questions in class.
Presentation: 30%
In-class presentation of relevant papers. Some paper suggestions to be posted shortly.
Project: 50%
Significant independent or group project. There will be a poster session at the end of the course for project presentations. Projects will also be evaluated based on midterm and final reports. More on this later...

Papers to be presented, in no particular order:

Casella, G., Robert, C.P. and Wells, M.T. (November, 2000) Rao-Blackwellization of Generalized Accept-Reject Schemes. pdf.

Simulating normalizing constants: from importance sampling to bridge sampling to path sampling. Andrew Gelman and Xiao-Li Meng pdf

Minimum variance importance sampling via population Monte Carlo. Douc, R., Guillin, A., Marin, J.M., and Robert, C.P., ESAIM Probability and Statistics (to appear). Available as pdf

Dirichlet Processes Tutorial.
Y.W. Teh. [slides.pdf]

A Bayesian Analysis of Some Nonparametric Problems. Thomas S. Ferguson. Annals of Statistics, Vol. 1, No. 2, (Mar., 1973). pdf

Ferguson Distributions Via Polya Urn Schemes. David Blackwell and James B. MacQueen.
Annals of Statistics, Vol. 1, No. 2, (Mar., 1973). pdf

Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems. Charles E. Antoniak.
Annals of Statistics, Vol. 2, No. 6, (Nov., 1974). pdf

A Constructive Definition of Dirichlet Priors. Jayaram Sethuraman. Statistica Sinica, Vol. 4, (1994). pdf

Gibbs sampling methods for stick-breaking priors. Hemant Ishwaran and Lancelot F. James. Journal of the American Statistical Association, March 2001, Vol. 96, No. 453, Theory and Methods. pdf

Infinite latent feature models and the Indian buffet process.Griffiths, T. L., Ghahramani, Z. (2006).Advances in Neural Information Processing Systems 18.(pdf) (journal)

Stick-breaking Construction for the Indian Buffet Process.
Y.W. Teh, D. Gorur and Z. Ghahramani. AISTATS 2007.
pdf]

Describing Visual Scenes Using Transformed Objects and Parts.
E. Sudderth, A. Torralba, W. Freeman, and A. Willsky. (pdf)

Generalizing Swendsen-Wang for Image Analysis. A. Barbu and S.C. Zhu
--- Journal of Computational and Graphical Statistics, vol. 16, no. 4, 877-900, 2007 [pdf]

A Hierarchical Bayesian Language Model based on Pitman-Yor Processes.
Y.W. Teh . ACL 2006. [pdf]

Clifford, P. and Nicholls, G. (November, 1995) A Metropolis Sampler for the Reconstruction of Polygonal Images.Available as Compressed Postscript. Abstract also available as Hypertext.

Fastest Mixing of Markov Chain on a Graph and a Connection to a Maximum Variance Unfolding Problem. With J. Sun, S. Boyd and L. Xiao. SIAM Review, 48(4):681-699. (2006). [PDF]

Nando de Freitas and Arnaud Doucet. Toward Practical N^2 Monte Carlo: The Marginal Particle Filter . UAI 2005. PDF

CIS 700 - Advanced Topics in Machine Learning - Spring 08 Monte Carlo Methods and Nonparametric Bayesian Models