Minimizing and Maximizing the Shannon Entropy for Fixed Marginals
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915481500254208 |
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| author | Franke, Paula Hamacher, Kay Manns, Paul |
| author_facet | Franke, Paula Hamacher, Kay Manns, Paul |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05099 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimizing and Maximizing the Shannon Entropy for Fixed Marginals Franke, Paula Hamacher, Kay Manns, Paul Optimization and Control 90C26, 90C90 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. |
| title | Minimizing and Maximizing the Shannon Entropy for Fixed Marginals |
| topic | Optimization and Control 90C26, 90C90 |
| url | https://arxiv.org/abs/2509.05099 |