Qualitative Mechanism Independence
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916584618983424 |
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| author | Richardson, Oliver E Peters, Spencer Halpern, Joseph Y |
| author_facet | Richardson, Oliver E Peters, Spencer Halpern, Joseph Y |
| contents | We define what it means for a joint probability distribution to be compatible with a set of independent causal mechanisms, at a qualitative level -- or, more precisely, with a directed hypergraph ${\mathcal{A}}$, which is the qualitative structure of a probabilistic dependency graph (PDG). When ${\mathcal{A}}$ represents a qualitative Bayesian network, QIM-compatibility with ${\mathcal{A}}$ reduces to satisfying the appropriate conditional independencies. But giving semantics to hypergraphs using QIM-compatibility lets us do much more. For one thing, we can capture functional dependencies. For another, we can capture important aspects of causality using compatibility: we can use compatibility to understand cyclic causal graphs, and to demonstrate structural compatibility, we must essentially produce a causal model. Finally, QIM-compatibility has deep connections to information theory. Applying our notion to cyclic structures helps to clarify a longstanding conceptual issue in information theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15488 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Qualitative Mechanism Independence Richardson, Oliver E Peters, Spencer Halpern, Joseph Y Information Theory We define what it means for a joint probability distribution to be compatible with a set of independent causal mechanisms, at a qualitative level -- or, more precisely, with a directed hypergraph ${\mathcal{A}}$, which is the qualitative structure of a probabilistic dependency graph (PDG). When ${\mathcal{A}}$ represents a qualitative Bayesian network, QIM-compatibility with ${\mathcal{A}}$ reduces to satisfying the appropriate conditional independencies. But giving semantics to hypergraphs using QIM-compatibility lets us do much more. For one thing, we can capture functional dependencies. For another, we can capture important aspects of causality using compatibility: we can use compatibility to understand cyclic causal graphs, and to demonstrate structural compatibility, we must essentially produce a causal model. Finally, QIM-compatibility has deep connections to information theory. Applying our notion to cyclic structures helps to clarify a longstanding conceptual issue in information theory. |
| title | Qualitative Mechanism Independence |
| topic | Information Theory |
| url | https://arxiv.org/abs/2501.15488 |