A Complete Diagrammatic Calculus for Conditional Gaussian Mixtures

2025/10/06 by Torres-Ruiz, Mateo, Piedeleu, Robin, Silva, Alexandra +1 · 1 citation
#FOS: Computer and information sciences #Logic in Computer Science (cs.LO)

paper · doi:10.48550/arxiv.2510.04649

Abstract

We extend the synthetic theories of discrete and Gaussian categorical probability by introducing a diagrammatic calculus for reasoning about hybrid probabilistic models in which continuous random variables, conditioned on discrete ones, follow a multivariate Gaussian distribution. This setting includes important classes of models such as Gaussian mixture models, where each Gaussian component is selected according to a discrete variable. We develop a string diagrammatic syntax for expressing and combining these models, give it a compositional semantics, and equip it with a sound and complete equational theory that characterises when two models represent the same distribution.

Citations

• An Algebraic Approach to Moralisation and Triangulation of Probabilistic Graphical Models
• A Complete Axiomatisation of Equivalence for Discrete Probabilistic Programming
• Graphical Quadratic Algebra
• An Introduction to String Diagrams for Computer Scientists
• Causal Inference by String Diagram Surgery
• The Logical Essentials of Bayesian Reasoning
• Causal Theories: A Categorical Perspective on Bayesian Networks

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