Markov category
Markov categories are copy-discard categories of total morphisms that have conditionals. From conditionals, we can prove the existence of Bayesian inversions. The main example is the category of distributions ( Stoch, the Kleisli category of the finitary distribution monad); continuous examples are given by standard Borel spaces (see Giry monad) and normal Gaussian noise (see Gaussian probability theory).
- conditional
- partial Markov category
- discrete partial Markov category
- First action of produoidal Markov split
- Second action of produoidal Markov split
- distributions that are marginally independent of the parameter
- divergence on a Markov category
Tags: probability, monoidal category.
References.
- Disintegration and Bayesian Inversion via String Diagrams (Cho, Jacobs, 2017)
- A Synthetic Approach to Markov Kernels (Fritz, 2020)
- Free GS-Monoidal Categories and Free Markov Categories (Fritz, Liang, 2023)
- Markov Categories and Entropy (Perrone, 2023)
- Representable Markov Categories and Comparison of Statistical Experiments in CAtegorical Probability (Fritz, Gonda, Perrone, Rischel, 2023)
- Dilations and information flow axioms in categorical probability (Fritz, Gonda, Houghton-Larsen, Perrone, Stein, 2022)
- Evidential Decision Theory via Partial Markov Categories (Di Lavore, Roman, 2023)
- Causal Inference by String Diagram Surgery (Jacobs, Kissinger, Zanasi)
- A Simple Formal Language for Probabilistic Decision Problems (Di Lavore, Jacobs, Román, 2024)