@article{baudart_reactive_2019,
title = {Reactive {Probabilistic} {Programming}},
url = {http://arxiv.org/abs/1908.07563},
abstract = {Synchronous reactive languages were introduced for designing and implementing real-time control software. These domain-specific languages allow for writing a modular and mathematically precise specification of the system, enabling a user to simulate, test, verify, and, finally, compile the system into executable code. However, to date these languages have had limited modern support for modeling uncertainty -- probabilistic aspects of the software's environment or behavior -- even though modeling uncertainty is a primary activity when designing a control system. In this paper we extend Z{\textbackslash}'elus, a synchronous programming language, to deliver ProbZ{\textbackslash}'elus, the first synchronous probabilistic programming language. ProbZ{\textbackslash}'elus is a probabilistic programming language in that it provides facilities for probabilistic models and inference: inferring latent model parameters from data. We present ProbZ{\textbackslash}'elus's measure-theoretic semantics in the setting of probabilistic, stateful stream functions. We then demonstrate a semantics-preserving compilation strategy to a first-order functional core calculus that lends itself to a simple semantic presentation of ProbZ{\textbackslash}'elus's inference algorithms. We also redesign the delayed sampling inference algorithm to provide bounded and streaming delayed sampling inference for ProbZ{\textbackslash}'elus models. Together with our evaluation on several reactive programs, our results demonstrate that ProbZ{\textbackslash}'elus provides efficient, bounded memory probabilistic inference.},
urldate = {2019-11-28},
journal = {arXiv:1908.07563 [cs]},
author = {Baudart, Guillaume and Mandel, Louis and Atkinson, Eric and Sherman, Benjamin and Pouzet, Marc and Carbin, Michael},
month = aug,
year = {2019},
note = {ZSCC: 0000001
arXiv: 1908.07563},
keywords = {Bayesian inference, Denotational semantics, Implementation, Probabilistic programming, Programming language theory}
}
@inproceedings{dal_lago_geometry_2019,
title = {The {Geometry} of {Bayesian} {Programming}},
doi = {10/ggdk85},
author = {Dal Lago, Ugo and Hoshino, Naohiko},
month = jun,
year = {2019},
note = {ZSCC: 0000000},
keywords = {Bayesian inference, Denotational semantics, Linear logic, Probabilistic programming, Programming language theory, Rewriting theory, Transition systems},
pages = {1--13}
}
@incollection{yang_commutative_2017,
address = {Berlin, Heidelberg},
title = {Commutative {Semantics} for {Probabilistic} {Programming}},
volume = {10201},
isbn = {978-3-662-54433-4 978-3-662-54434-1},
url = {http://link.springer.com/10.1007/978-3-662-54434-1_32},
abstract = {We show that a measure-based denotational semantics for probabilistic programming is commutative. The idea underlying probabilistic programming languages (Anglican, Church, Hakaru, ...) is that programs express statistical models as a combination of prior distributions and likelihood of observations. The product of prior and likelihood is an unnormalized posterior distribution, and the inference problem is to ﬁnd the normalizing constant. One common semantic perspective is thus that a probabilistic program is understood as an unnormalized posterior measure, in the sense of measure theory, and the normalizing constant is the measure of the entire semantic domain.},
language = {en},
urldate = {2019-11-23},
booktitle = {Programming {Languages} and {Systems}},
publisher = {Springer Berlin Heidelberg},
author = {Staton, Sam},
editor = {Yang, Hongseok},
year = {2017},
doi = {10.1007/978-3-662-54434-1_32},
note = {ZSCC: NoCitationData[s0] },
keywords = {Bayesianism, Probabilistic programming, Programming language theory, Semantics},
pages = {855--879}
}
@article{staton_semantics_2016,
title = {Semantics for probabilistic programming: higher-order functions, continuous distributions, and soft constraints},
shorttitle = {Semantics for probabilistic programming},
url = {http://arxiv.org/abs/1601.04943},
doi = {10/ggdf97},
abstract = {We study the semantic foundation of expressive probabilistic programming languages, that support higher-order functions, continuous distributions, and soft constraints (such as Anglican, Church, and Venture). We define a metalanguage (an idealised version of Anglican) for probabilistic computation with the above features, develop both operational and denotational semantics, and prove soundness, adequacy, and termination. They involve measure theory, stochastic labelled transition systems, and functor categories, but admit intuitive computational readings, one of which views sampled random variables as dynamically allocated read-only variables. We apply our semantics to validate nontrivial equations underlying the correctness of certain compiler optimisations and inference algorithms such as sequential Monte Carlo simulation. The language enables defining probability distributions on higher-order functions, and we study their properties.},
urldate = {2019-11-23},
journal = {Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '16},
author = {Staton, Sam and Yang, Hongseok and Heunen, Chris and Kammar, Ohad and Wood, Frank},
year = {2016},
note = {ZSCC: 0000071
arXiv: 1601.04943},
keywords = {Bayesianism, Probabilistic programming, Programming language theory, Semantics},
pages = {525--534}
}