Bart Jacobs ; Dario Stein - Pearl's and Jeffrey's Update as Modes of Learning in Probabilistic Programming

entics:12281 - Electronic Notes in Theoretical Informatics and Computer Science, November 23, 2023, Volume 3 - Proceedings of MFPS XXXIX -
Pearl's and Jeffrey's Update as Modes of Learning in Probabilistic ProgrammingArticle

Authors: Bart Jacobs ; Dario Stein

    The concept of updating a probability distribution in the light of new evidence lies at the heart of statistics and machine learning. Pearl's and Jeffrey's rule are two natural update mechanisms which lead to different outcomes, yet the similarities and differences remain mysterious. This paper clarifies their relationship in several ways: via separate descriptions of the two update mechanisms in terms of probabilistic programs and sampling semantics, and via different notions of likelihood (for Pearl and for Jeffrey). Moreover, it is shown that Jeffrey's update rule arises via variational inference. In terms of categorical probability theory, this amounts to an analysis of the situation in terms of the behaviour of the multiset functor, extended to the Kleisli category of the distribution monad.

    Volume: Volume 3 - Proceedings of MFPS XXXIX
    Published on: November 23, 2023
    Accepted on: October 16, 2023
    Submitted on: September 16, 2023
    Keywords: Computer Science - Logic in Computer Science,Computer Science - Artificial Intelligence

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