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Delayed Sampling and Automatic Rao-Blackwellization of Probabilistic Programs
Uppsala University.
KTH, School of Electrical Engineering and Computer Science (EECS), Software and Computer systems, SCS.
Uppsala University.
KTH, School of Electrical Engineering and Computer Science (EECS), Software and Computer systems, SCS.ORCID iD: 0000-0001-8457-4105
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2018 (English)In: Proceeding of the 21st International Conference on Artificial Intelligence and Statistics (AISTATS 2018), PMLR , 2018Conference paper, Published paper (Refereed)
Abstract [en]

We introduce a dynamic mechanism for the solution of analytically-tractable substructure in probabilistic programs, using conjugate priors and affine transformations to reduce variance in Monte Carlo estimators. For inference with Sequential Monte Carlo, this automatically yields improvements such as locally-optimal proposals and Rao–Blackwellization. The mechanism maintains a directed graph alongside the running program that evolves dynamically as operations are triggered upon it. Nodes of the graph represent random variables, edges the analytically-tractable relationships between them. Random variables remain in the graph for as long as possible, to be sampled only when they are used by the program in a way that cannot be resolved analytically. In the meantime, they are conditioned on as many observations as possible. We demonstrate the mechanism with a few pedagogical examples, as well as a linear-nonlinear state-space model with simulated data, and an epidemiological model with real data of a dengue outbreak in Micronesia. In all cases one or more variables are automatically marginalized out to significantly reduce variance in estimates of the marginal likelihood, in the final case facilitating a random-weight or pseudo-marginal-type importance sampler for parameter estimation. We have implemented the approach in Anglican and a new probabilistic programming language called Birch.

Place, publisher, year, edition, pages
PMLR , 2018.
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:kth:diva-261169Scopus ID: 2-s2.0-85056483781OAI: oai:DiVA.org:kth-261169DiVA, id: diva2:1356912
Conference
International Conference on Artificial Intelligence and Statistics (AISTATS)21st International Conference on Artificial Intelligence and Statistics, AISTATS 2018; Playa Blanca, Lanzarote, Canary Islands; Spain; 9 April 2018 through 11 April 2018
Note

QC 20191002

Available from: 2019-10-02 Created: 2019-10-02 Last updated: 2019-10-02Bibliographically approved

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