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POPL 2019
Sun 13 - Sat 19 January 2019 Cascais, Portugal
Wed 16 Jan 2019 14:07 - 14:29 at Sala I - Probabilistic Programming and Semantics Chair(s): Justin Hsu

We give an adequate denotational semantics for languages with recursive higher-order types, continuous probability distributions, and soft constraints. These are expressive languages for building Bayesian models of the kinds used in computational statistics and machine learning. Among them are untyped languages, similar to Church and WebPPL, because our semantics allows recursive mixed-variance datatypes. Our semantics justifies important program equivalences including commutativity.

Our new semantic model is based on `quasi-Borel predomains’. These are a mixture of chain-complete partial orders (cpos) and quasi-Borel spaces. Quasi-Borel spaces are a recent model of probability theory that focuses on sets of admissible random elements. Probability is traditionally treated in cpo models using probabilistic powerdomains, but these are not known to be commutative on any class of cpos with higher order functions. By contrast, quasi-Borel predomains do support both a commutative probabilistic powerdomain and higher-order functions. As we show, quasi-Borel predomains form both a model of Fiore’s axiomatic domain theory and a model of Kock’s synthetic measure theory.

A Domain Theory for Statistical Probabilistic Programming - slides (popl-2019.pdf)2.36MiB

Wed 16 Jan
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13:45 - 14:51
Probabilistic Programming and SemanticsResearch Papers at Sala I
Chair(s): Justin HsuUniversity of Wisconsin-Madison, USA
13:45
22m
Talk
Probabilistic Programming with Densities in SlicStan: Efficient, Flexible and Deterministic
Research Papers
Maria I. GorinovaThe University of Edinburgh, Andrew D. GordonMicrosoft Research and University of Edinburgh, Charles SuttonUniversity of Edinburgh
Link to publication DOI Pre-print Media Attached File Attached
14:07
22m
Talk
A Domain Theory for Statistical Probabilistic ProgrammingDistinguished Paper
Research Papers
Matthijs VákárUniversity of Oxford, Ohad KammarUniversity of Edinburgh, Sam StatonUniversity of Oxford
Link to publication DOI Pre-print Media Attached File Attached
14:29
22m
Talk
Bayesian Synthesis of Probabilistic Programs for Automatic Data Modeling
Research Papers
Feras A. SaadMassachusetts Institute of Technology, Marco Cusumano-TownerMIT-CSAIL, Ulrich SchaechtleMassachusetts Institute of Technology, USA, Martin C. RinardMassachusetts Institute of Technology, Vikash K. MansinghkaMIT
Link to publication DOI Media Attached File Attached