This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.

Abstract Details

Activity Number: 401
Type: Topic Contributed
Date/Time: Tuesday, August 3, 2010 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #308090
Title: Entropy and Divergence Estimation for High-Dimensional Data
Author(s): Kumar Sricharan*+ and Raviv Raich and Alfred O. Hero
Companies: University of Michigan and Oregon State University and University of Michigan
Address: , Ann Arbor, MI, 48109,
Keywords: entropy estimation ; divergence estimation ; kNN graphs ; nonparametric estimation
Abstract:

Entropy and divergence estimation is an important task in statistical signal processing. Several estimators have been proposed in literature and while they have been shown to be consistent, results on rates of convergence are in general unavailable. We propose a simple class of estimators based on proximity graphs to estimate entropy and divergence for high dimensional data. Our class of estimators exploit a close relation between density estimation and the geometry of proximity neighborhoods in the data sample. For our class of estimators, we will present (i) an asymptotic analysis of the bias and variance and (ii) results on weak convergence. These results are useful for choosing tuning parameters and for predicting fundamental performance limits. We will apply our theory to diverse applications including image registration, intrinsic dimension estimation and structure discovery.


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