[Ml-stat-talks] Wilks Statistics Seminar on Friday Nov. 7: Omer Brobowski (Duke) on topological data analysis

Philippe Rigollet rigollet at Princeton.EDU
Wed Oct 29 14:42:14 EDT 2014


The next speaker in the Wilks statistics seminar will be Omer Brobowski from Duke.
http://www.math.duke.edu/~omer/
If you would like to meet with Omer, please contact Alex Furger afurger at Princeton.EDU<mailto:afurger at Princeton.EDU>
Philippe
------------
Time: Friday, Nov. 7, 12:30pm

Location: Sherrerd Hall 101

Title: Topological Consistency via Kernel Estimation

Abstract: Let X_1,X_2,..., X_n be iid random variables in d-dimensional Euclidean space, generated by an unknown probability density function f. The level sets of the density function are of a considerable interest in many areas of statistics. Previous work focused on recovering the level sets of f, minimizing local measures such as the Hausdorff distance or the symmetric distance. We will focus on global features related to the topology of level sets. In particular, we are interested in the homology of these sets. Briefly, homology is an algebraic structure describing the topology of a set in terms of connected components and holes.

The main difficulty in recovering the homology is that even small perturbations to the estimated density function can generate a very large error. In this talk we discuss these problems, and present an estimator that overcomes these difficulties. We then show that this estimator is consistent, and discuss possible applications for clustering and topological manifold learning.

• This talk assumes no prior knowledge in algebraic topology.
--
Philippe Rigollet
www.princeton.edu/~rigollet<http://www.princeton.edu/~rigollet>



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