Affine Monads and Lazy Structures for Bayesian Programming
Abstract
We show that streams and lazy data structures are a natural idiom for programming with infinite-dimensional Bayesian methods such as Poisson processes, Gaussian processes, jump processes, Dirichlet processes, and Beta processes. The crucial semantic idea, inspired by developments in synthetic probability theory, is to work with two separate monads: an affine monad of probability, which supports laziness, and a commutative, non-affine monad of measures, which does not. (Affine means that T (1)≅ 1.) We show that the separation is important from a decidability perspective, and that the recent model of quasi-Borel spaces supports these two monads.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 09, 2023
- Source ID
- 10.1145/3571239
Entities
People
- Hugo Paquet
- Sam Staton
- Swaraj Dash
- Younesse Kaddar
Organizations
- Air Force Office of Scientific Research
- European Research Council
- University of Oxford