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Probabilistic Programming with Stochastic Probabilities

Authors:

Alexander K. Lew,

Matin Ghavamizadeh,

Martin C. Rinard,

Vikash K. MansinghkaAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 7, Issue PLDI

Article No.: 176, Pages 1708 - 1732

https://doi.org/10.1145/3591290

Published: 06 June 2023 Publication History

Abstract

We present a new approach to the design and implementation of probabilistic programming languages (PPLs), based on the idea of stochastically estimating the probability density ratios necessary for probabilistic inference. By relaxing the usual PPL design constraint that these densities be computed exactly, we are able to eliminate many common restrictions in current PPLs, to deliver a language that, for the first time, simultaneously supports first-class constructs for marginalization and nested inference, unrestricted stochastic control flow, continuous and discrete sampling, and programmable inference with custom proposals. At the heart of our approach is a new technique for compiling these expressive probabilistic programs into randomized algorithms for unbiasedly estimating their densities and density reciprocals. We employ these stochastic probability estimators within modified Monte Carlo inference algorithms that are guaranteed to be sound despite their reliance on inexact estimates of density ratios. We establish the correctness of our compiler using logical relations over the semantics of λ_SP, a new core calculus for modeling and inference with stochastic probabilities. We also implement our approach in an open-source extension to Gen, called GenSP, and evaluate it on six challenging inference problems adapted from the modeling and inference literature. We find that: (1) ‍can automate fast density estimators for programs with very expensive exact densities; (2) convergence of inference is mostly unaffected by the noise from these estimators; and (3) our sound-by-construction estimators are competitive with hand-coded density estimators, incurring only a small constant-factor overhead.

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Cited By

Becker MLew AWang XGhavami MHuot MRinard MMansinghka V(2024)Probabilistic Programming with Programmable Variational InferenceProceedings of the ACM on Programming Languages10.1145/36564638:PLDI(2123-2147)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656463
Li JWang EZhang Y(2024)Compiling Probabilistic Programs for Variable Elimination with Information FlowProceedings of the ACM on Programming Languages10.1145/36564488:PLDI(1755-1780)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656448
Huot MGhavami MLew ASchaechtle UFreer CShelby ZRinard MSaad FMansinghka V(2024)GenSQL: A Probabilistic Programming System for Querying Generative Models of Database TablesProceedings of the ACM on Programming Languages10.1145/36564098:PLDI(790-815)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656409

Index Terms

Probabilistic Programming with Stochastic Probabilities
1. Mathematics of computing
  1. Mathematical software
    1. Statistical software
  2. Probability and statistics
    1. Probabilistic inference problems
      1. Bayesian computation
2. Software and its engineering
  1. Software notations and tools
    1. Compilers
    2. Formal language definitions

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cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 7, Issue PLDI

June 2023

2020 pages

EISSN:2475-1421

DOI:10.1145/3554310

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Michael Hicks
Amazon, USA

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Published: 06 June 2023

Published in PACMPL Volume 7, Issue PLDI

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Cited By

Becker MLew AWang XGhavami MHuot MRinard MMansinghka V(2024)Probabilistic Programming with Programmable Variational InferenceProceedings of the ACM on Programming Languages10.1145/36564638:PLDI(2123-2147)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656463
Li JWang EZhang Y(2024)Compiling Probabilistic Programs for Variable Elimination with Information FlowProceedings of the ACM on Programming Languages10.1145/36564488:PLDI(1755-1780)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656448
Huot MGhavami MLew ASchaechtle UFreer CShelby ZRinard MSaad FMansinghka V(2024)GenSQL: A Probabilistic Programming System for Querying Generative Models of Database TablesProceedings of the ACM on Programming Languages10.1145/36564098:PLDI(790-815)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656409

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