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• W2949804971 abstract "We develop the operational semantics of an untyped probabilistic λ-calculus with continuous distributions, and both hard and soft constraints,as a foundation for universal probabilistic programming languages such as Church, Anglican, and Venture. Our first contribution is to adapt the classic operational semantics of λ-calculus to a continuous setting via creating a measure space on terms and defining step-indexed approximations. We prove equivalence of big-step and small-step formulations of this distribution-based semantics . To move closer to inference techniques, we also define the sampling-based semantics of a term as a function from a trace of random samples to a value. We show that the distribution induced by integration over the space of traces equals the distribution-based semantics. Our second contribution is to formalize the implementation technique of trace Markov chain Monte Carlo (MCMC) for our calculus and to show its correctness. A key step is defining sufficient conditions for the distribution induced by trace MCMC to converge to the distribution-based semantics. To the best of our knowledge, this is the first rigorous correctness proof for trace MCMC for a higher-order functional language, or for a language with soft constraints." @default.
• W2949804971 created "2019-06-27" @default.
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• W2949804971 date "2016-09-04" @default.
• W2949804971 modified "2023-09-26" @default.
• W2949804971 title "A lambda-calculus foundation for universal probabilistic programming" @default.
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• W2949804971 doi "https://doi.org/10.1145/3022670.2951942" @default.
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