Measure Transformer Semantics for Bayesian Machine Learning

Johannes Borgstrom, Andrew D. Gordon, Michael Greenberg, James Margetson, Jurgen Van Gael

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract / Description of output

The Bayesian approach to machine learning amounts to inferring posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables. There is a trend in machine learning towards expressing Bayesian models as probabilistic programs. As a foundation for this kind of programming, we propose a core functional calculus with primitives for sampling prior distributions and observing variables. We define combinators for measure transformers, based on theorems in measure theory, and use these to give a rigorous semantics to our core calculus. The original features of our semantics include its support for discrete, continuous, and hybrid measures, and, in particular, for observations of zero-probability events. We compile our core language to a small imperative language that has a straightforward semantics via factor graphs, data structures that enable many efficient inference algorithms. We use an existing inference engine for efficient approximate inference of posterior marginal distributions, treating thousands of observations per second for large instances of realistic models.
Original languageEnglish
Title of host publicationProgramming Languages and Systems
Subtitle of host publication20th European Symposium on Programming, ESOP 2011, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2011, Saarbrücken, Germany, March 26–April 3, 2011. Proceedings
EditorsGilles Barthe
PublisherSpringer-Verlag GmbH
Pages77-96
Number of pages20
ISBN (Electronic)978-3-642-19718-5
ISBN (Print)978-3-642-19717-8
DOIs
Publication statusPublished - 2011

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Berlin / Heidelberg
Volume6602

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