Inference of entropies of discrete random variables with unknown cardinalities

We examine the recently introduced NSB estimator of entropies of severely undersampled discrete variables and devise a procedure for calculating the involved integrals. We discover that the output of the estimator has a well defined limit for large cardinalities of the variables being studied. Thus one can estimate entropies with no a priori assumptions about these cardinalities, and a closed form solution for such estimates is given.

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