Compositional semantics for probabilistic programs with exact conditioning

Conference item

We define a probabilistic programming language for Gaussian random variables with a first-class exact conditioning construct. We give operational, denotational and equational semantics for this language, establishing convenient properties like exchangeability of conditions. Conditioning on equality of continuous random variables is nontrivial, as the exact observation may have probability zero; this is Borel's paradox. Using categorical formulations of conditional probability, we show that the good properties of our language are not particular to Gaussians, but can be derived from universal properties, thus generalizing to wider settings. We define the Cond construction, which internalizes conditioning as a morphism, providing general compositional semantics for probabilistic programming with exact conditioning.

Authors: Stein, D; Staton, S

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IEEE
• Host title: Proceedings of the Annual ACM/IEEE Symposium on Logic in Computer Science
• Pages: 1-13
• Publication date: 2021-07-07
• Acceptance date: 2021-04-30
• Event title: 36th Annual Symposium on Logic in Computer Science (LICS 2021)
• Event location: Online
• Event website: http://lics.siglog.org/
• Event start date: 2021-06-29
• Event end date: 2021-07-02
• DOI: 10.1109/LICS52264.2021.9470552
• EISBN: 978-1-6654-4895-6
• ISBN: 978-1-6654-4896-3
• Language: English
• Keywords: FFR