{"ID":2874243,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.05099","arxiv_id":"2509.05099","title":"Minimizing and Maximizing the Shannon Entropy for Fixed Marginals","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.","short_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...","url_abs":"https://arxiv.org/abs/2509.05099","url_pdf":"https://arxiv.org/pdf/2509.05099v1","authors":"[\"Paula Franke\",\"Kay Hamacher\",\"Paul Manns\"]","published":"2025-09-05T13:36:38Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}