Semantics for probabilistic programming: higher-order functions, continuous distributions, and soft constraints

Conference item

We study the semantic foundation of expressive probabilistic programming languages, that support higher-order functions, continuous distributions, and soft constraints (such as Anglican, Church, and Venture). We define a metalanguage (an idealised version of Anglican) for probabilistic computation with the above features, develop both operational and denotational semantics, and prove soundness, adequacy, and termination. They involve measure theory, stochastic labelled transition systems, and functor categories, but admit intuitive computational readings, one of which views sampled random variables as dynamically allocated read-only variables. We apply our semantics to validate nontrivial equations underlying the correctness of certain compiler optimisations and inference algorithms such as sequential Monte Carlo simulation. The language enables defining probability distributions on higher-order functions, and we study their properties.

Authors: Yang, H; Staton, S; Wood, F; Heunen, C; Kammar, O

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Association for Computing Machinery
• Host title: LICS '16 Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science
• Journal: LICS 2016: Thirty-First Annual ACM/IEEE Symposium on Logic in Computer Science
• Pages: 525-534
• Publication date: 2016-07-05
• Acceptance date: 2016-04-04
• DOI: 10.1145/2933575.2935313
• ISBN: 9781450343916