2021/09/09 by Toby St Clere Smithe, Smithe, Toby St. Clere · 1 citation
Arts and Humanities · Computer Science · #Adaptation and Self-Organizing Systems (nlin.AO) #Category Theory (math.CT) #Computability, Logic, AI Algorithms #FOS: Mathematics #FOS: Physical sciences #Machine Learning and Algorithms #Philosophy and History of Science #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2109.04461
openalex publication_date 2021/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.