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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.08279 |
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| _version_ | 1866912977106501632 |
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| author | Guo, Laigang Yeung, Raymond W. Guo, Tao |
| author_facet | Guo, Laigang Yeung, Raymond W. Guo, Tao |
| contents | Conditional independence, and more generally conditional mutual independence, are central notions in probability theory. In their general forms, they include functional dependence as a special case. In this paper, we tackle two fundamental problems related to conditional mutual independence. Let $K$ and $K'$ be two conditional mutual independncies (CMIs) defined on a finite set of discrete random variables. We have obtained a necessary and sufficient condition for i) $K$ is equivalent to $K'$; ii) $K$ implies $K'$. These characterizations are in terms of a canonical form introduced for conditional mutual independence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08279 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characterizations of Conditional Mutual Independence: Equivalence and Implication Guo, Laigang Yeung, Raymond W. Guo, Tao Probability Information Theory Conditional independence, and more generally conditional mutual independence, are central notions in probability theory. In their general forms, they include functional dependence as a special case. In this paper, we tackle two fundamental problems related to conditional mutual independence. Let $K$ and $K'$ be two conditional mutual independncies (CMIs) defined on a finite set of discrete random variables. We have obtained a necessary and sufficient condition for i) $K$ is equivalent to $K'$; ii) $K$ implies $K'$. These characterizations are in terms of a canonical form introduced for conditional mutual independence. |
| title | Characterizations of Conditional Mutual Independence: Equivalence and Implication |
| topic | Probability Information Theory |
| url | https://arxiv.org/abs/2602.08279 |