Towards a Compositional Framework for Convex Analysis (with Applications to Probability Theory)

Autor:	Stein, Dario, Samuelson, Richard
Rok vydání:	2023
Předmět:	Mathematics - Category Theory Mathematics - Optimization and Control 18M35 (Primary) 52A41 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We introduce a compositional framework for convex analysis based on the notion of convex bifunction of Rockafellar. This framework is well-suited to graphical reasoning, and exhibits rich dualities such as the Legendre-Fenchel transform, while generalizing formalisms like graphical linear algebra, convex relations and convex programming. We connect our framework to probability theory by interpreting the Laplace approximation in its context: The exactness of this approximation on normal distributions means that logdensity is a functor from Gaussian probability (densities and integration) to concave bifunctions and maximization. Comment: 21 pages, 1 figure, submitted to FoSSaCS 2024
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2312.02291 Zobrazit plný text záznamu View this record from Arxiv