@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{jacobs_formal_2017,
title = {A {Formal} {Semantics} of {Influence} in {Bayesian} {Reasoning}},
url = {http://drops.dagstuhl.de/opus/volltexte/2017/8089/},
doi = {10/ggdgbc},
abstract = {This paper proposes a formal deﬁnition of inﬂuence in Bayesian reasoning, based on the notions of state (as probability distribution), predicate, validity and conditioning. Our approach highlights how conditioning a joint entwined/entangled state with a predicate on one of its components has ‘crossover’ inﬂuence on the other components. We use the total variation metric on probability distributions to quantitatively measure such inﬂuence. These insights are applied to give a rigorous explanation of the fundamental concept of d-separation in Bayesian networks.},
language = {en},
urldate = {2019-11-24},
journal = {Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany},
author = {Jacobs, Bart and Zanasi, Fabio},
year = {2017},
note = {ZSCC: 0000012},
keywords = {Bayesianism, Categorical probability theory, Programming language theory, Semantics}
}
@article{jacobs_predicate/state_2016,
series = {The {Thirty}-second {Conference} on the {Mathematical} {Foundations} of {Programming} {Semantics} ({MFPS} {XXXII})},
title = {A {Predicate}/{State} {Transformer} {Semantics} for {Bayesian} {Learning}},
volume = {325},
issn = {1571-0661},
url = {http://www.sciencedirect.com/science/article/pii/S1571066116300883},
doi = {10/ggdgbb},
abstract = {This paper establishes a link between Bayesian inference (learning) and predicate and state transformer operations from programming semantics and logic. Specifically, a very general definition of backward inference is given via first applying a predicate transformer and then conditioning. Analogously, forward inference involves first conditioning and then applying a state transformer. These definitions are illustrated in many examples in discrete and continuous probability theory and also in quantum theory.},
language = {en},
urldate = {2019-11-24},
journal = {Electronic Notes in Theoretical Computer Science},
author = {Jacobs, Bart and Zanasi, Fabio},
month = oct,
year = {2016},
note = {ZSCC: 0000030},
keywords = {Bayesianism, Categorical ML, Categorical probability theory, Effectus theory, Programming language theory, Semantics},
pages = {185--200}
}
@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}
}