{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/delayed-sampling-and-automatic-rao","title":"Delayed Sampling and Automatic Rao-Blackwellization of Probabilistic Programs","arxiv_id":"1708.07787","date":"2017-08-25","proceeding":null,"authors":["Lawrence M. Murray","Daniel Lundén","Jan Kudlicka","David Broman","Thomas B. Schön"],"abstract":"We introduce a dynamic mechanism for the solution of analytically-tractable\nsubstructure in probabilistic programs, using conjugate priors and affine\ntransformations to reduce variance in Monte Carlo estimators. For inference\nwith Sequential Monte Carlo, this automatically yields improvements such as\nlocally-optimal proposals and Rao-Blackwellization. The mechanism maintains a\ndirected graph alongside the running program that evolves dynamically as\noperations are triggered upon it. Nodes of the graph represent random\nvariables, edges the analytically-tractable relationships between them. Random\nvariables remain in the graph for as long as possible, to be sampled only when\nthey are used by the program in a way that cannot be resolved analytically. In\nthe meantime, they are conditioned on as many observations as possible. We\ndemonstrate the mechanism with a few pedagogical examples, as well as a\nlinear-nonlinear state-space model with simulated data, and an epidemiological\nmodel with real data of a dengue outbreak in Micronesia. In all cases one or\nmore variables are automatically marginalized out to significantly reduce\nvariance in estimates of the marginal likelihood, in the final case\nfacilitating a random-weight or pseudo-marginal-type importance sampler for\nparameter estimation. We have implemented the approach in Anglican and a new\nprobabilistic programming language called Birch.","url_abs":"http://arxiv.org/abs/1708.07787v2","url_pdf":"http://arxiv.org/pdf/1708.07787v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"delayed-sampling-and-automatic-rao","repo_url":"https://github.com/pyro-ppl/funsor","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"delayed-sampling-and-automatic-rao","repo_url":"https://github.com/2023-MindSpore-4/Code6/tree/main/RAOD","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"delayed-sampling-and-automatic-rao","repo_url":"https://github.com/Mind23-2/MindCode-5/tree/main/RAOD","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"mindspore","reach":null},{"paper_slug":"delayed-sampling-and-automatic-rao","repo_url":"https://github.com/MindSpore-paper-code-2/code2/tree/main/RAOD","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"mindspore","reach":null},{"paper_slug":"delayed-sampling-and-automatic-rao","repo_url":"https://github.com/code-implementation1/Code6/tree/main/RAOD","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"mindspore","reach":null}],"tasks":[{"task_slug":"probabilistic-programming","task_name":"Probabilistic Programming"},{"task_slug":"parameter-estimation","task_name":"parameter estimation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1708.07787","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1708.07787"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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