Graphical Quadratic Algebra

Dario Stein; Fabio Zanasi; Robin Piedeleu; Richard Samuelson

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arXiv · 2403.02284

Graphical Quadratic Algebra

Dario Stein·Fabio Zanasi·Robin Piedeleu·Richard Samuelson

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Abstract

Convex analysis and Gaussian probability are tightly connected, as mostly evident in the theory of linear regression. Our work introduces an algebraic perspective on such relationship, in the form of a diagrammatic calculus of string diagrams, called Graphical Quadratic Algebra (GQA). We show that GQA is a complete axiomatisation for the category of quadratic relations, a compositional formulation of quadratic problems. Moreover, we identify a sub-theory of GQA which is complete for the category of Gaussian probabilistic processes. We show how GQA may be used to study linear regression and probabilistic programming.

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Dario Stein, Fabio Zanasi, Robin Piedeleu, Richard Samuelson. 2024-03-04. Graphical Quadratic Algebra. https://arxiv.org/abs/2403.02284

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