Dilations and information flow axioms in categorical probability
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866917017082134528 |
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| author | Fritz, Tobias Gonda, Tomáš Houghton-Larsen, Nicholas Gauguin Lorenzin, Antonio Perrone, Paolo Stein, Dario |
| author_facet | Fritz, Tobias Gonda, Tomáš Houghton-Larsen, Nicholas Gauguin Lorenzin, Antonio Perrone, Paolo Stein, Dario |
| contents | We study the positivity and causality axioms for Markov categories as properties of dilations and information flow in Markov categories, and in variations thereof for arbitrary semicartesian monoidal categories. These help us show that being a positive Markov category is merely an additional property of a symmetric monoidal category (rather than extra structure). We also characterize the positivity of representable Markov categories and prove that causality implies positivity, but not conversely. Finally, we note that positivity fails for quasi-Borel spaces and interpret this failure as a privacy property of probabilistic name generation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_02507 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Dilations and information flow axioms in categorical probability Fritz, Tobias Gonda, Tomáš Houghton-Larsen, Nicholas Gauguin Lorenzin, Antonio Perrone, Paolo Stein, Dario Category Theory Information Theory Logic in Computer Science Probability 18M05, 18D10, 60A05, 68Q55, 03B70 We study the positivity and causality axioms for Markov categories as properties of dilations and information flow in Markov categories, and in variations thereof for arbitrary semicartesian monoidal categories. These help us show that being a positive Markov category is merely an additional property of a symmetric monoidal category (rather than extra structure). We also characterize the positivity of representable Markov categories and prove that causality implies positivity, but not conversely. Finally, we note that positivity fails for quasi-Borel spaces and interpret this failure as a privacy property of probabilistic name generation. |
| title | Dilations and information flow axioms in categorical probability |
| topic | Category Theory Information Theory Logic in Computer Science Probability 18M05, 18D10, 60A05, 68Q55, 03B70 |
| url | https://arxiv.org/abs/2211.02507 |