Measure transformer semantics for Bayesian machine learning

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

43 Scopus citations

Abstract

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 - 20th European Symposium on Programming, ESOP 2011, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2011, Proceedings
Pages77-96
Number of pages20
DOIs
StatePublished - 2011
Event20th European Symposium on Programming, ESOP 2011, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2011 - Saarbrucken, Germany
Duration: 26 Mar 20113 Apr 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6602 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference20th European Symposium on Programming, ESOP 2011, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2011
Country/TerritoryGermany
CitySaarbrucken
Period26/03/113/04/11

Fingerprint

Dive into the research topics of 'Measure transformer semantics for Bayesian machine learning'. Together they form a unique fingerprint.

Cite this