The Magmoid of Normalized Stochastic Kernels
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866908799468568576 |
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| author | Di Lavore, Elena Román, Mario Széles, Márk |
| author_facet | Di Lavore, Elena Román, Mario Széles, Márk |
| contents | Normalization, $D(X + 1) \to D(X) + 1$, is almost a distributive law; but because one of the distributive law axioms only holds up-to-idempotent, it yields a non-associative composition of normalized kernels. We introduce the Markov magmoid of normalized stochastic kernels: a normalized-by-construction semantics for probabilistic inference, unifying exact Bayesian observations and interventions as two parenthesizations of the same composite. Front-door and back-door criteria follow from the axioms of Markov magmoids; we implement these with non-associative monadic notation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01131 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Magmoid of Normalized Stochastic Kernels Di Lavore, Elena Román, Mario Széles, Márk Category Theory 18M99 Normalization, $D(X + 1) \to D(X) + 1$, is almost a distributive law; but because one of the distributive law axioms only holds up-to-idempotent, it yields a non-associative composition of normalized kernels. We introduce the Markov magmoid of normalized stochastic kernels: a normalized-by-construction semantics for probabilistic inference, unifying exact Bayesian observations and interventions as two parenthesizations of the same composite. Front-door and back-door criteria follow from the axioms of Markov magmoids; we implement these with non-associative monadic notation. |
| title | The Magmoid of Normalized Stochastic Kernels |
| topic | Category Theory 18M99 |
| url | https://arxiv.org/abs/2510.01131 |