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Mathematics > Statistics Theory

arXiv:2109.04461 (math)
[Submitted on 9 Sep 2021 (v1), last revised 8 Jun 2022 (this version, v2)]

Title:Compositional Active Inference I: Bayesian Lenses. Statistical Games

Authors:Toby St. Clere Smithe
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Abstract:We introduce the concepts of Bayesian lens, characterizing the bidirectional structure of exact Bayesian inference, and statistical game, formalizing the optimization objectives of approximate inference problems. We prove that Bayesian inversions compose according to the compositional lens pattern, and exemplify statistical games with a number of classic statistical concepts, from maximum likelihood estimation to generalized variational Bayesian methods. This paper is the first in a series laying the foundations for a compositional account of the theory of active inference, and we therefore pay particular attention to statistical games with a free-energy objective.
Comments: v2: updated definition of context; minor corrections. 31 pages. Comments welcome
Subjects: Statistics Theory (math.ST); Category Theory (math.CT); Adaptation and Self-Organizing Systems (nlin.AO)
Cite as: arXiv:2109.04461 [math.ST]
  (or arXiv:2109.04461v2 [math.ST] for this version)
  https://doi.org/10.48550/arXiv.2109.04461

Submission history

From: Toby St. Clere Smithe [view email]
[v1] Thu, 9 Sep 2021 17:57:43 UTC (188 KB)
[v2] Wed, 8 Jun 2022 18:26:48 UTC (2,694 KB)
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