Asymptotic Bias in Information Estimates and the Exponential (Bell) Polynomials

Authors:
Jonathan D. Victor
Affiliations:
Department of Neurology and Neuroscience, Weill Medical College of Cornell University, New York City, New York 10021, U.S.A.
Venue:
Neural Computation
Year:
2000

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Abstract

We present a new derivation of the asymptotic correction for bias in the estimate of information from a finite sample. The new derivation reveals a relationship between information estimates and a sequence of polynomials with combinatorial significance, the exponential (Bell) polynomials, and helps to provide an understanding of the form and behavior of the asymptotic correction for bias.