Normalization as a distributive law
Normalization is a candidate distributive law between the maybe monad and the distribution monad. It forms an almost distributive law, but it is not a distributive law.
See also.
- renormalize whenever
- normalization is not a distributive law
- normalization is a distributive law up to idempotent
- Norm, the Kleisli unital magmoid of partial stochastic functions
- subdistributions act on the normalization magmoid
- normalization is monoidal
Normalization in partial Markov categories
Normalizations exist in any partial Markov category and they follow from conditionals. They are only almost surely unique; and almost surely idempotent. The renormalization formula can be proven in any partial Markov category.
See also.
- normalisations are almost surely idempotent
- normalization is almost a restriction operator, normalization fails r4 in subdistributions.
- normalization of a composition
- renormalize whenever
Literature
- Semantics for Probabilistic Programming, Higher-Order Functions, Continuous Distributions, and Soft Constraints (Staton, Yang, Wood, Heunen, Kammar, 2016) mentions renormalization as a program transformation that increases efficiency.
Tags: partial Markov category.