Compositional Active Inference I: Bayesian Lenses. Statistical Games — Toby St. Clere Smithe (2021). arXiv:2109.04461 (v2, PDF).
Develops Bayesian lenses over copy-delete categories (via Grothendieck lenses and actegories) and defines statistical games as Bayesian lenses paired with fitness functions on contexts, with monoidal categories of games and examples including maximum likelihood, Bayesian inference, free energy and autoencoders.
Sources: the paper, arXiv:2109.04461v2, checked against the arXiv listing. Index: Papers.
Key definitions and results
- Definitions 2.35–2.38: Grothendieck lenses; Propositions 2.43–2.47: Para via actegories
- Definition 3.7, Theorem 3.14: Bayesian lenses and exact inversion composes
- Proposition 4.11: categories of statistical games
- Definitions 5.8–5.11, Proposition 5.10: KL, D-free energy, evidence upper bound
- Examples 5.3–5.17: maximum likelihood, Bayesian inference, autoencoders, generalized Bayesian inference
Concept notes
Statistical Game, Bayesian Lens, Variational Free Energy, Copy-Discard Category