Dimensionality, granularity, and differential residual weighted entropy

Tunnicliffe, Martin and Hunter, Gordon (2019) Dimensionality, granularity, and differential residual weighted entropy. Entropy, 21(9), p. 825. ISSN (online) 1099-4300


While Shannon’s differential entropy adequately quantifies a dimensioned random variable’s information deficit under a given measurement system, the same cannot be said of differential weighted entropy in its existing formulation. We develop weighted and residual weighted entropies of a dimensioned quantity from their discrete summation origins, exploring the relationship between their absolute and differential forms, and thus derive a “differentialized” absolute entropy based on a chosen “working granularity” consistent with Buckingham’s Π-theorem. We apply this formulation to three common continuous distributions: exponential, Gaussian, and gamma and consider policies for optimizing the working granularity.

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