[2309.07053] Pearl's and Jeffrey's Update as Modes of Learning in Probabilistic Programming
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arXiv:2309.07053 (cs)
[Submitted on 13 Sep 2023 (v1), last revised 18 Nov 2023 (this version, v2)]

Title:Pearl's and Jeffrey's Update as Modes of Learning in Probabilistic Programming

Authors:Bart Jacobs, Dario Stein
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Abstract: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.
Subjects: Logic in Computer Science (cs.LO); Artificial Intelligence (cs.AI)
Cite as: arXiv:2309.07053 [cs.LO]
  (or arXiv:2309.07053v2 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.2309.07053
Journal reference: Electronic Notes in Theoretical Informatics and Computer Science, Volume 3 - Proceedings of MFPS XXXIX (November 23, 2023) entics:12281
Related DOI: https://doi.org/10.46298/entics.12281

Submission history

From: Michael Mislove [view email]
[v1] Wed, 13 Sep 2023 16:09:13 UTC (62 KB)
[v2] Sat, 18 Nov 2023 20:17:39 UTC (68 KB)
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