On the Intersection and Composition properties of conditional independence
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910196813529088 |
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| author | Boege, Tobias |
| author_facet | Boege, Tobias |
| contents | Compositional graphoids are fundamental discrete structures which appear in probabilistic reasoning, particularly in the area of graphical models. They are semigraphoids which satisfy the Intersection and Composition properties. These important properties, however, are not enjoyed by general probability distributions. This paper surveys what is known about them, providing systematic constructions of examples and counterexamples as well as necessary and sufficient conditions. Novel sufficient conditions for both properties are derived in the context of discrete random variables via information-theoretic tools. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11978 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Intersection and Composition properties of conditional independence Boege, Tobias Information Theory Statistics Theory 94A15 (primary) 62R01, 94A17 (secondary) Compositional graphoids are fundamental discrete structures which appear in probabilistic reasoning, particularly in the area of graphical models. They are semigraphoids which satisfy the Intersection and Composition properties. These important properties, however, are not enjoyed by general probability distributions. This paper surveys what is known about them, providing systematic constructions of examples and counterexamples as well as necessary and sufficient conditions. Novel sufficient conditions for both properties are derived in the context of discrete random variables via information-theoretic tools. |
| title | On the Intersection and Composition properties of conditional independence |
| topic | Information Theory Statistics Theory 94A15 (primary) 62R01, 94A17 (secondary) |
| url | https://arxiv.org/abs/2504.11978 |