Entropy, Derivation Operators and Huffman Trees

Simon Burton

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arXiv · 2107.11208

Entropy, Derivation Operators and Huffman Trees

Simon Burton

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Abstract

We build a theory of binary trees on finite multisets that categorifies, or operationalizes, the entropy of a finite probability distribution. Multisets operationalize probabilities as the event outcomes of an experiment. Huffman trees operationalize the entropy of the distribution of these events. We show how the derivation property of the entropy of a joint distribution lifts to Huffman trees.

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Simon Burton. 2021-07-23. Entropy, Derivation Operators and Huffman Trees. https://arxiv.org/abs/2107.11208

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