Graphical Quadratic Algebra
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915475576848384 |
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| author | Stein, Dario Zanasi, Fabio Piedeleu, Robin Samuelson, Richard |
| author_facet | Stein, Dario Zanasi, Fabio Piedeleu, Robin Samuelson, Richard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02284 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graphical Quadratic Algebra Stein, Dario Zanasi, Fabio Piedeleu, Robin Samuelson, Richard Logic in Computer Science Category Theory Optimization and Control G.3; F.3.2; F.4.0 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. |
| title | Graphical Quadratic Algebra |
| topic | Logic in Computer Science Category Theory Optimization and Control G.3; F.3.2; F.4.0 |
| url | https://arxiv.org/abs/2403.02284 |