Report
Graphical Quadratic Algebra
| العنوان: | Graphical Quadratic Algebra |
|---|---|
| المؤلفون: | Stein, Dario, Zanasi, Fabio, Piedeleu, Robin, Samuelson, Richard |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Computer Science - Logic in Computer Science, Mathematics - Category Theory, Mathematics - Optimization and Control, G.3, F.3.2, F.4.0 |
| الوصف: | We introduce Graphical Quadratic Algebra (GQA), a string diagrammatic calculus extending the language of Graphical Affine Algebra with a new generator characterised by invariance under rotation matrices. We show that GQA is a sound and complete axiomatisation for three different models: quadratic relations, which are a compositional formalism for least-squares problems, Gaussian stochastic processes, and Gaussian stochastic processes extended with non-determinisms. The equational theory of GQA sheds light on the connections between these perspectives, giving an algebraic interpretation to the interplay of stochastic behaviour, relational behaviour, non-determinism, and conditioning. As applications, we discuss various case studies, including linear regression, probabilistic programming, and electrical circuits with realistic (noisy) components. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.02284 |
| رقم الانضمام: | edsarx.2403.02284 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |