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info.json
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info.json
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{
"abstract": "The d-separation criterion detects the compatibility of a joint probability distribution with a directed acyclic graph through certain conditional independences. In this work, we study this problem in the context of categorical probability theory by introducing a categorical definition of causal models, a categorical notion of d-separation, and proving an abstract version of the d-separation criterion. This approach has two main benefits. First, categorical d-separation is a very intuitive criterion based on topological connectedness. Second, our results apply both to measure-theoretic probability (with standard Borel spaces) and beyond probability theory, including to deterministic and possibilistic networks. It therefore provides a clean proof of the equivalence of local and global Markov properties with causal compatibility for continuous and mixed random variables as well as deterministic and possibilistic variables.",
"authors": [
"Tobias Fritz",
"Andreas Klingler"
],
"emails": [
"tobias.fritz@uibk.ac.at",
"andreas.klingler@uibk.ac.at"
],
"id": "22-0916",
"issue": 46,
"pages": [
1,
49
],
"title": "The d-Separation Criterion in Categorical Probability",
"volume": 24,
"year": 2023
}