A method for estimating Shannon differential entropy is proposed based on the second order expansion of the probability mass around the inspection point with respect to the distance from the point. Polynomial regression with Poisson error structure is utilized to estimate the values of density function. The density estimates at every given data points are averaged to obtain entropy estimators. The proposed estimator is shown to perform well through numerical experiments for various probability distributions.
CITATION STYLE
Hino, H., Akaho, S., & Murata, N. (2016). An entropy estimator based on polynomial regression with poisson error structure. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9948 LNCS, pp. 11–19). Springer Verlag. https://doi.org/10.1007/978-3-319-46672-9_2
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