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Proceedings Paper

Robust entropy estimation strategies based on edge weighted random graphs
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Paper Abstract

In this paper we treat the problem of robust entropy estimation given a multidimensional random sample from an unknown distribution. In particular, we consider estimation of the Renyi entropy of fractional order which is insensitive to outliers, e.g. high variance contaminating distributions, using the k-point minimal spanning tree. A greedy algorithm for approximating the NP-hard problem of computing the k-minimal spanning tree is given which is a generalization of the potential function partitioning method of Ravi et al. The basis for our approach is asymptotic theorem establishing that the log of the overall length or weight of the greedy approximation is a strongly consistent estimator of the Renyi entropy. Quantitative robustness of the estimator to outliers is established using Hampel's method of influence functions. The structure of the influence function indicates that the k-MST is a natural extension of the 1D, (alpha) -trimmed mean for multi- dimensional data.

Paper Details

Date Published: 22 September 1998
PDF: 12 pages
Proc. SPIE 3459, Bayesian Inference for Inverse Problems, (22 September 1998);
Show Author Affiliations
Alfred O. Hero III, Univ. of Michigan (United States)
Olivier Michel, Ecole Normale Superieure de Lyon (France)

Published in SPIE Proceedings Vol. 3459:
Bayesian Inference for Inverse Problems
Ali Mohammad-Djafari, Editor(s)

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