Probabilistic Programming with Densities in SlicStan: Efficient, Flexible, and Deterministic

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Abstract

Stan is a probabilistic programming language that has been increasingly used for real-world scalable projects. However, to make practical inference possible, the language sacrifices some of its usability by adopting a block syntax, which lacks compositionality and flexible user-defined functions. Moreover, the semantics of the language has been mainly given in terms of intuition about implementation, and has not been formalised.

This paper provides a formal treatment of the Stan language, and introduces the probabilistic programming language SlicStan --- a compositional, self-optimising version of Stan. Our main contributions are (1) the formalisation of a core subset of Stan through an operational density-based semantics; (2) the design and semantics of the Stan-like language SlicStan, which facilities better code reuse and abstraction through its compositional syntax, more flexible functions, and information-flow type system; and (3) a formal, semantic-preserving procedure for translating SlicStan to Stan.
Original languageEnglish
Article number35
Pages (from-to)35:1-35:30
Number of pages30
JournalProceedings of the ACM on Programming Languages
Volume3
Issue numberPOPL
DOIs
Publication statusPublished - 2 Jan 2019

Keywords

  • information flow analysis
  • probabilistic programming
  • Markov chain Monte Carlo method
  • probabilistic computing

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