# Evidential Decision Theory via Partial Markov Categories

arXiv: https://arxiv.org/abs/2301.12989 · HTML: https://mlsanity.com/paper/2301.12989/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2023.

## Built on by (most cited first, 2 of 2)

- [Towards Compositional Interpretability for XAI](https://mlsanity.com/paper/2406.17583/) (2024)
- [Active Inference in String Diagrams: A Categorical Account of Predictive Processing and Free Energy](https://mlsanity.com/paper/2308.00861/) (2023)

## Abstract (arXiv)

We introduce partial Markov categories. In the same way that Markov categories encode stochastic processes, partial Markov categories encode stochastic processes with constraints, observations and updates. In particular, we prove a synthetic Bayes theorem and we apply it to define a syntactic partial theory of observations on any Markov category, whose normalisations can be computed in the original Markov category. Finally, we formalise Evidential Decision Theory in terms of partial Markov categories, and provide implemented examples.