Dilations and information flow axioms in categorical probability
T. A. Fritz, Tomáš Gonda, Nicholas Gauguin Houghton-Larsen, Antonio Lorenzin, Paolo Perrone, Dario Stein
Abstract
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.
Topics & Concepts
Property (philosophy)AxiomCausality (physics)Categorical variableMathematicsProbabilistic logicMarkov chainMarkov propertyInformation flowPure mathematicsFlow (mathematics)Mathematical economicsDiscrete mathematicsTheoretical computer scienceComputer scienceLinguisticsMarkov modelStatisticsEpistemologyPhilosophyPhysicsQuantum mechanicsGeometryLogic, Reasoning, and KnowledgeDistributed systems and fault toleranceComputability, Logic, AI Algorithms