A Category for unifying Gaussian Probability and Nondeterminism — Dario Stein & Richard Samuelson (2022). arXiv:2204.14024 (v2, PDF).
Introduces extended Gaussian distributions (a nondeterministic subspace plus a Gaussian on the quotient) and the Markov category GaussEx, proves it has conditionals, and obtains Gaussian relations as a hypergraph category into which Gaussian-decorated cospans map — unifying Gaussian noise, linear constraints and uninformative priors, after Willems’ open stochastic systems.
Sources: the paper, arXiv:2204.14024v2, checked against the arXiv listing. Index: Papers.
Key definitions and results
- Definition 3: extended Gaussian distribution
- Definitions 8, 11: extended Gaussian maps, GaussEx
- Theorem 13: GaussEx has conditionals
- Theorem 14: a hypergraph functor from Gaussian-decorated cospans to Gaussian relations
Concept notes
Gaussian Relations, Hypergraph Category, Markov Category, Conditionals and Disintegration