Minimizing and Maximizing the Shannon Entropy for Fixed Marginals

Paula Franke; Kay Hamacher; Paul Manns

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arXiv · 2509.05099

Minimizing and Maximizing the Shannon Entropy for Fixed Marginals

Paula Franke·Kay Hamacher·Paul Manns

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Abstract

The mutual information (MI) between two random variables is an important correlation measure in data analysis. The Shannon entropy of a joint probability distribution is the variable part under fixed marginals. We aim to minimize and maximize it to obtain the largest and smallest MI possible in this case, leading to a scaled MI ratio for better comparability. We present algorithmic approaches and optimal solutions for a set of problem instances based on data from molecular evolution. We show that this allows us to construct a sensible, systematic correction to raw MI values.

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BibTeX RIS

Paula Franke, Kay Hamacher, Paul Manns. 2025-09-05. Minimizing and Maximizing the Shannon Entropy for Fixed Marginals. https://arxiv.org/abs/2509.05099

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