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Guaranteed Bounds for Posterior Inference in Universal Probabilistic Programming

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conference contribution
posted on 2023-11-29, 18:21 authored by Raven BeutnerRaven Beutner, C. H. Luke Ong, Fabian Zaiser
We propose a new method to approximate the posterior distribution of probabilistic programs by means of computing guaranteed bounds. The starting point of our work is an interval-based trace semantics for a recursive, higher-order probabilistic programming language with continuous distributions. Taking the form of (super-/subadditive) measures, these lower/upper bounds are non-stochastic and provably correct: using the semantics, we prove that the actual posterior of a given program is sandwiched between the lower and upper bounds (soundness); moreover, the bounds converge to the posterior (completeness). As a practical and sound approximation, we introduce a weight-aware interval type system, which automatically infers interval bounds on not just the return value but also the weight of program executions, simultaneously. We have built a tool implementation, called GuBPI, which automatically computes these posterior lower/upper bounds. Our evaluation on examples from the literature shows that the bounds are useful, and can even be used to recognise wrong outputs from stochastic posterior inference procedures.

History

Preferred Citation

Raven Beutner, C. Ong and Fabian Zaiser. Guaranteed Bounds for Posterior Inference in Universal Probabilistic Programming. In: ACM-SIGPLAN Conference on Programming Language Design and Implementation (PLDI). 2022.

Primary Research Area

  • Reliable Security Guarantees

Name of Conference

ACM-SIGPLAN Conference on Programming Language Design and Implementation (PLDI)

Legacy Posted Date

2022-06-01

Open Access Type

  • Green

BibTeX

@inproceedings{cispa_all_3704, title = "Guaranteed Bounds for Posterior Inference in Universal Probabilistic Programming", author = "Beutner, Raven and Ong, C. H. Luke and Zaiser, Fabian", booktitle="{ACM-SIGPLAN Conference on Programming Language Design and Implementation (PLDI)}", year="2022", }

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