research-article

A model-learner pattern for bayesian reasoning

Authors:

Andrew D. Gordon,

Mihhail Aizatulin,

Johannes Borgstrom,

Guillaume Claret,

Aditya V. Nori,

Sriram K. Rajamani, and

Claudio RussoAuthors Info & Claims

ACM SIGPLAN Notices, Volume 48, Issue 1

Pages 403 - 416

https://doi.org/10.1145/2480359.2429119

Published: 23 January 2013 Publication History

Abstract

A Bayesian model is based on a pair of probability distributions, known as the prior and sampling distributions. A wide range of fundamental machine learning tasks, including regression, classification, clustering, and many others, can all be seen as Bayesian models. We propose a new probabilistic programming abstraction, a typed Bayesian model, which is based on a pair of probabilistic expressions for the prior and sampling distributions. A sampler for a model is an algorithm to compute synthetic data from its sampling distribution, while a learner for a model is an algorithm for probabilistic inference on the model. Models, samplers, and learners form a generic programming pattern for model-based inference. They support the uniform expression of common tasks including model testing, and generic compositions such as mixture models, evidence-based model averaging, and mixtures of experts. A formal semantics supports reasoning about model equivalence and implementation correctness. By developing a series of examples and three learner implementations based on exact inference, factor graphs, and Markov chain Monte Carlo, we demonstrate the broad applicability of this new programming pattern.

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Index Terms

A model-learner pattern for bayesian reasoning
1. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language features
        Patterns

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Published In

cover image ACM SIGPLAN Notices

ACM SIGPLAN Notices Volume 48, Issue 1

POPL '13

January 2013

561 pages

ISSN:0362-1340

EISSN:1558-1160

DOI:10.1145/2480359

Issue’s Table of Contents

POPL '13: Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
January 2013
586 pages
ISBN:9781450318327
DOI:10.1145/2429069
General Chair:
Roberto Giacobazzi
Università di Verona, Italy
,
Program Chair:
Radhia Cousot
École normale supérieure CNRS & INRIA, France

Copyright © 2013 ACM.

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Publication History

Published: 23 January 2013

Published in SIGPLAN Volume 48, Issue 1

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https://dl.acm.org/doi/10.1145/3585391
Chatterjee KGoharshady ENovotný PZárevúcky JŽikelić Đ(2021)On Lexicographic Proof Rules for Probabilistic TerminationFormal Methods10.1007/978-3-030-90870-6_33(619-639)Online publication date: 20-Nov-2021
https://dl.acm.org/doi/10.1007/978-3-030-90870-6_33
Wang PFu HGoharshady AChatterjee KQin XShi WMcKinley KFisher K(2019)Cost analysis of nondeterministic probabilistic programsProceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation10.1145/3314221.3314581(204-220)Online publication date: 8-Jun-2019
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