Mathematical Foundations for a Compositional Account of the Bayesian Brain — Toby St Clere Smithe (2022). arXiv:2212.12538 (v3, PDF).
Doctoral thesis supplying functorial semantics for approximate inference: Bayesian lenses, fibrations of statistical games whose sections classify inference problems (relative entropy as a strict section; maximum likelihood and free energy as lax sections), copy-composition by coparameterization, and a general formalisation of open dynamical systems via polynomial functors.
Sources: the paper, arXiv:2212.12538v3, checked against the arXiv listing. Index: Papers.
Key definitions and results
- §5.2.1: copy-composition by coparameterization ()
- §5.2.3–5.2.4: coparameterized Bayesian lenses compose optically
- Fibrations of statistical games and their (lax) sections
Concept notes
Statistical Game, Open Model, Bayesian Lens, Para Construction, Grothendieck Construction