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Entropy estimation using the principle of maximum entropy

TitleEntropy estimation using the principle of maximum entropy
Publication TypeConference Paper
Year of Publication2011
AuthorsBehmardi, B., R. Raich, and A. O. Hero, III
Conference NameICASSP 2011 - 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
Pagination2008 - 2011
Date Published05/2011
Conference LocationPrague, Czech Republic
ISBN Number978-1-4577-0538-0
Keywordsentropy estimation, m-term approximation, maximum entropy

In this paper, we present a novel entropy estimator for a given set of samples drawn from an unknown probability density function (PDF). Counter to other entropy estimators, the estimator presented here is parametric. The proposed estimator uses the maximum entropy principle to offer an to-term approximation to the underlying distribution and does not rely on local density estimation. The accuracy of the proposed algorithm is analyzed and it is shown that the estimation error is ≤ O(√(log n/n)). In addition to the analytic results, a numerical evaluation of the estimator on synthetic data as well as on experimental sensor network data is provided. We demonstrate a significant improvement in accuracy relative to other methods.