AutoBayes: A Compositional Framework for Generalized Variational Inference — Toby St Clere Smithe & Marco Perin (2025). arXiv:2503.18608 (v2, PDF).
Introduces a compositional framework in which approximate Bayesian inference is assembled from local pieces, like automatic differentiation. Models are open models whose composition files intermediate variables into a latent space instead of integrating them out; attaching approximate inversions gives Bayesian lenses; adding an energy and an entropy gives statistical games, whose losses (generalised free energies) satisfy a chain rule. Parameterized games and a lax composition of gradients complete the picture, and the appendix recovers maximum likelihood, EM, variational Bayesian EM, supervised learning and Bayesian deep learning as wirings.
Sources: the paper, arXiv:2503.18608v2, checked against the arXiv listing. Index: Papers.
Key definitions and results
- Definitions 1–8: open models, sequential and parallel composition, copiers, cups and caps (self-dual compact closed)
- Definitions 9–12, Theorem 13: Bayesian lenses and the chain rule for open models
- Definition 15, Remark 16: parallel composition of inversions is lax
- Definition 17, Proposition 18: variational free energy in three forms
- Definition 20: statistical game; Definition 22 and Theorem 23: energies add, entropies chain, free energy obeys a chain rule
- Remark 24: priors as games; Remark 26: laxness = mutual information
- Definitions 27–29, Remark 30: parameterized games, composition of gradients, lax sections of a fibration
- Appendix A: Examples 1–5
Concept notes
Open Model, Bayesian Lens, Bayesian Inversion, Variational Free Energy, Statistical Game, Lax Functor, Compact Closed Category
Used in Lenticulum.jl
Factors are Parameterized Statistical Games · AutoBayes to Lenticulum · Scalar and Multivariate Energy