TY - JOUR
TI - A Formal Semantics of Influence in Bayesian Reasoning
AU - Jacobs, Bart
AU - Zanasi, Fabio
T2 - Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany
AB - 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.
DA - 2017///
PY - 2017
DO - 10/ggdgbc
DP - DataCite
LA - en
UR - http://drops.dagstuhl.de/opus/volltexte/2017/8089/
Y2 - 2019/11/24/12:11:15
KW - Bayesianism
KW - Categorical probability theory
KW - Programming language theory
KW - Semantics
ER -
TY - JOUR
TI - A Predicate/State Transformer Semantics for Bayesian Learning
AU - Jacobs, Bart
AU - Zanasi, Fabio
T2 - Electronic Notes in Theoretical Computer Science
T3 - The Thirty-second Conference on the Mathematical Foundations of Programming Semantics (MFPS XXXII)
AB - 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.
DA - 2016/10/05/
PY - 2016
DO - 10/ggdgbb
DP - ScienceDirect
VL - 325
SP - 185
EP - 200
J2 - Electronic Notes in Theoretical Computer Science
LA - en
SN - 1571-0661
UR - http://www.sciencedirect.com/science/article/pii/S1571066116300883
Y2 - 2019/11/24/12:04:12
KW - Bayesianism
KW - Categorical ML
KW - Categorical probability theory
KW - Effectus theory
KW - Programming language theory
KW - Semantics
ER -
TY - JOUR
TI - Semantics for probabilistic programming: higher-order functions, continuous distributions, and soft constraints
AU - Staton, Sam
AU - Yang, Hongseok
AU - Heunen, Chris
AU - Kammar, Ohad
AU - Wood, Frank
T2 - Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '16
AB - 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.
DA - 2016///
PY - 2016
DO - 10/ggdf97
DP - arXiv.org
SP - 525
EP - 534
ST - Semantics for probabilistic programming
UR - http://arxiv.org/abs/1601.04943
Y2 - 2019/11/23/16:36:30
KW - Bayesianism
KW - Probabilistic programming
KW - Programming language theory
KW - Semantics
ER -