Nesting Probabilistic Programs

By Tom Rainforth. 2018

25 citations recorded by the source corpus.

We formalize the notion of nesting probabilistic programming queries and investigate the resulting statistical implications. We demonstrate that while query nesting allows the definition of models which could not otherwise be expressed, such as those involving agents reasoning about other agents, existing systems take approaches which lead to inconsistent estimates. We show how to correct this by delineating possible ways one might want to nest queries and asserting the respective conditions required for convergence. We further introduce a new online nested Monte Carlo estimator that makes it substantially easier to ensure these conditions are met, thereby providing a simple framework for designing statistically correct inference engines. We prove the correctness of this online estimator and show that, when using the recommended setup, its asymptotic variance is always better than that of the equivalent fixed estimator, while its bias is always within a factor of two.

Subfields: Artificial Intelligence, Probabilistic & Bayesian Methods

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Citations in the corpus

An Introduction to Probabilistic Programming (2018, background): “(2018) warnings about convergence rates for nested sampling and also utilize sampling methodologies that are specifically tailored to this situation (Rainforth, 2018; Naesseth et al., 2015).”
On Nesting Monte Carlo Estimators (2017, methodology): “As we show in Rainforth (2017; 2018), the results presented here can be brought to bear on assessing the relative correctness of the different ways PPSs allow model nesting.”
Efficient Probabilistic Inference in the Quest for Physics Beyond the Standard Model (2018, background): “Efficient handling of rejection sampling in universal PPLs [45, 69], and nested inference in general [76, 77], constitute an active area of research with several alternative approaches currently being formulated with varying degrees of complexity and sample efficiency that are beyond the scope of th”