2006-07 Program on High Dimensional Inference and Random Matrices

Intructor Names: Misha Belkin, Sayan Mukherjee, and Yury Mileyko
Course Day and Time: Thursday 4:30 - 7:00, beginning January 11, 2007
Room 104 NISS Building

From the perspective of inference, clustering, and machine learning, geometric ideas have been gaining greater emphasis. One reason for this has been the realization that predictive models with a small amount of labelled data can be greatly improved by incorporating unlabelled data. Thus the geometry of the marginal distribution provides salient and compelling information in many real world problems.

This insight has lead to a variety of statistical models and algorithms as well as the study of a variety of mathematical objects. A nonexhaustive list follows: spectral clustering, nonlinear dimensionality reduction,manifold learning, learning homologies, topological persistence, semi-supervised learning, non-parametric semi-supervised Bayesian models, the Laplace-Beltrami operator, graph diffusion models on manifolds, random projections. Most if not all of the above topics are intimately related to the study of random matrices either from an algorithmic perspective or from the perspective that the structure of a random matrix depending on data drawn from a measure is fundamental in understanding the topic.

These topics will be presented from the perspective of Statisticians, Computer Scientists, and Mathematicians.

The course will start with a lightning review of statistical inference, topology, and differential geometry and then proceed to seminars. There will be a final project consisting of any of the following:

1. paper review
2. algorithm/model development
3. data analysis
4. theoretical analysis

Duke Course Listing STA 294.02
NCSU Course Listing MA 810G.003, ST 810G.004 UNC Course Listing Math 891-002 (Instructor listed as STAFF)

Questions about the course or the Random Matrices program should be emailed to [email protected].

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