2023/12/04 by Dario Stein, Stein, Dario, Richard Samuelson +1
Computer Science · Arts and Humanities · #Bayesian Modeling and Causal Inference #Philosophy and History of Science #Logic, Reasoning, and Knowledge
paper · pdf · doi:10.48550/arxiv.2312.02291
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.