A category theory framework for Bayesian learning
This provides a theoretical foundation for Bayesian learning, but it is incremental as it builds on existing category theory works.
The paper tackles the problem of formalizing Bayesian inference and learning by introducing a categorical framework based on category theory, resulting in categorical formulations of batch and sequential Bayes updates and showing their coincidence in a specific example.
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.