Graphical Quadratic Algebra

Understand

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.