Fritz, Tobias;
Gonda, Tomáš;
Houghton-Larsen, Nicholas Gauguin;
Lorenzin, Antonio;
Perrone, Paolo;
Stein, Dario;
(2023)
Dilations and information flow axioms in categorical probability.
Mathematical Structures in Computer Science
, 33
(10)
pp. 913-957.
10.1017/S0960129523000324.
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Fritz Gonda Houghton-Larsen Lorenzin Perrone Stein - Dilations and information flow axioms in categorical probability.pdf - Accepted Version Download (617kB) | Preview |
Abstract
We study the positivity and causality axioms for Markov categories as properties of dilations and information flow and also develop 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.
| Type: | Article |
|---|---|
| Title: | Dilations and information flow axioms in categorical probability |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1017/S0960129523000324 |
| Publisher version: | https://doi.org/10.1017/s0960129523000324 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Categorical probability; Markov category; Semicartesian category; Information flow; Quasi-Borel space |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10206634 |
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