Stein, D;
Zanasi, F;
Piedeleu, R;
Samuelson, R;
(2025)
Graphical Quadratic Algebra.
In:
Theoretical Aspects of Computing – ICTAC 2025.
(pp. pp. 298-316).
Springer: Cham, Switzerland.
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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 relationships, 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.
| Type: | Proceedings paper |
|---|---|
| Title: | Graphical Quadratic Algebra |
| Event: | ICTAC 2025: 22nd International Colloquium |
| ISBN-13: | 9783032111753 |
| DOI: | 10.1007/978-3-032-11176-0_18 |
| Publisher version: | https://doi.org/10.1007/978-3-032-11176-0_18 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | String diagrams, categorical semantics, linear algebra, linear regression, categorical probability |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10219224 |
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