# A category theory framework for Bayesian learning

arXiv: https://arxiv.org/abs/2111.14293 · HTML: https://mlsanity.com/paper/2111.14293/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 13 references that are in the map.
- First posted on arXiv 29 Nov 2021.

## Builds on (most cited first, 4 of 4)

- [A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics](https://mlsanity.com/paper/1908.07021/) (2019)
- [Backprop as Functor: A compositional perspective on supervised learning](https://mlsanity.com/paper/1711.10455/) (2017)
- [Categorical Foundations of Gradient-Based Learning](https://mlsanity.com/paper/2103.01931/) (2021)
- [Disintegration and Bayesian Inversion via String Diagrams](https://mlsanity.com/paper/1709.00322/) (2017)

## Built on by (most cited first, 1 of 1)

- [Space-time tradeoffs of lenses and optics via higher category theory](https://mlsanity.com/paper/2209.09351/) (2022)

## Abstract (arXiv)

Inspired by the foundational works by Spivak and Fong and Cruttwell et al., we introduce a categorical framework to formalize Bayesian inference and learning. The two key ideas at play here are the notions of Bayesian inversions and the functor GL as constructed by Cruttwell et al.. In this context, we find that Bayesian learning is the simplest case of the learning paradigm. We then obtain categorical formulations of batch and sequential Bayes updates while also verifying that the two coincide in a specific example.