2026-08-07T09:01:01Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:18810 2024-03-06T11:01:55Z ddc:004 open_access

A Category for Unifying Gaussian Probability and Nondeterminism Stein, Dario Samuelson, Richard systems theory hypergraph categories Bayesian inference category theory Markov categories We introduce categories of extended Gaussian maps and Gaussian relations which unify Gaussian probability distributions with relational nondeterminism in the form of linear relations. Both have crucial and well-understood applications in statistics, engineering, and control theory, but combining them in a single formalism is challenging. It enables us to rigorously describe a variety of phenomena like noisy physical laws, Willems' theory of open systems and uninformative priors in Bayesian statistics. The core idea is to formally admit vector subspaces D ⊆ X as generalized uniform probability distribution. Our formalism represents a first bridge between the literature on categorical systems theory (signal-flow diagrams, linear relations, hypergraph categories) and notions of probability theory. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Dario Stein and Richard Samuelson 2023 Is Part Of LIPIcs, Volume 270, 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CALCO.2023.13 urn:nbn:de:0030-drops-188107 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2023.13 eng https://creativecommons.org/licenses/by/4.0/legalcode