Measure Transformer Semantics for Bayesian Machine Learning
2011 (English)In: 20th European Symposium on Programming: Held as Part of the Joint European Conferences on Theory and Practice of Software / [ed] G. Barthe, Berlin, Heidelberg: Springer-Verlag , 2011, 77-96 p.Conference paper (Refereed)
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.
Place, publisher, year, edition, pages
Berlin, Heidelberg: Springer-Verlag , 2011. 77-96 p.
, Lecture Notes in Computer Science, ISSN 0302-9743 ; 6602
IdentifiersURN: urn:nbn:se:uu:diva-161498DOI: 10.1007/978-3-642-19718-5_5OAI: oai:DiVA.org:uu-161498DiVA: diva2:456362
ESOP 2011, 20th European Symposium on Programming, Saarbrücken, Germany