[Ml-stat-talks] ReminderL Wilks Statistics Seminar TODAY: Omer Brobowski (Duke) on topological data analysis
Philippe Rigollet
rigollet at Princeton.EDU
Fri Nov 7 11:42:27 EST 2014
Reminder, today @ 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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