Dexter Kozen ; Alexandra Silva ; Erik Voogd - Joint Distributions in Probabilistic Semantics

entics:12279 - Electronic Notes in Theoretical Informatics and Computer Science, November 23, 2023, Volume 3 - Proceedings of MFPS XXXIX - https://doi.org/10.46298/entics.12279
Joint Distributions in Probabilistic SemanticsArticle

Authors: Dexter Kozen ; Alexandra Silva ; Erik Voogd

    Various categories have been proposed as targets for the denotational semantics of higher-order probabilistic programming languages. One such proposal involves joint probability distributions (couplings) used in Bayesian statistical models with conditioning. In previous treatments, composition of joint measures was performed by disintegrating to obtain Markov kernels, composing the kernels, then reintegrating to obtain a joint measure. Disintegrations exist only under certain restrictions on the underlying spaces. In this paper we propose a category whose morphisms are joint finite measures in which composition is defined without reference to disintegration, allowing its application to a broader class of spaces. The category is symmetric monoidal with a pleasing symmetry in which the dagger structure is a simple transpose.


    Volume: Volume 3 - Proceedings of MFPS XXXIX
    Published on: November 23, 2023
    Accepted on: October 16, 2023
    Submitted on: September 15, 2023
    Keywords: Computer Science - Programming Languages
    Funding:
      Source : OpenAIRE Graph
    • SHF: Small: Semantics of Higher Order Probabilistic Programs; Funder: National Science Foundation; Code: 2008083

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