A Complete Diagrammatic Calculus for Conditional Gaussian Mixtures
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918154848960512 |
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| author | Torres-Ruiz, Mateo Piedeleu, Robin Silva, Alexandra Zanasi, Fabio |
| author_facet | Torres-Ruiz, Mateo Piedeleu, Robin Silva, Alexandra Zanasi, Fabio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04649 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Complete Diagrammatic Calculus for Conditional Gaussian Mixtures Torres-Ruiz, Mateo Piedeleu, Robin Silva, Alexandra Zanasi, Fabio Logic in Computer Science 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. |
| title | A Complete Diagrammatic Calculus for Conditional Gaussian Mixtures |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2510.04649 |