# On the Role of Priors in Bayesian Causal Learning

arXiv: https://arxiv.org/abs/2504.01424 · HTML: https://mlsanity.com/paper/2504.01424/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 15 references that are in the map.
- First posted on arXiv 2 Apr 2025.

## Builds on (most cited first, 7 of 7)

- [Causality for Machine Learning](https://mlsanity.com/paper/1911.10500/) (2019)
- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Causal Direction of Data Collection Matters: Implications of Causal and Anticausal Learning for NLP](https://mlsanity.com/paper/2110.03618/) (2021)
- [Semi-Supervised Learning, Causality and the Conditional Cluster Assumption](https://mlsanity.com/paper/1905.12081/) (2019)
- [Semi-Generative Modelling: Covariate-Shift Adaptation with Cause and Effect Features](https://mlsanity.com/paper/1807.07879/) (2018)
- [On Causality in Domain Adaptation and Semi-Supervised Learning: an Information-Theoretic Analysis for Parametric Models](https://mlsanity.com/paper/2205.04641/) (2022)

## Abstract (arXiv)

In this work, we investigate causal learning of independent causal mechanisms from a Bayesian perspective. Confirming previous claims from the literature, we show in a didactically accessible manner that unlabeled data (i.e., cause realizations) do not improve the estimation of the parameters defining the mechanism. Furthermore, we observe the importance of choosing an appropriate prior for the cause and mechanism parameters, respectively. Specifically, we show that a factorized prior results in a factorized posterior, which resonates with Janzing and Sch"olkopf's definition of independent causal mechanisms via the Kolmogorov complexity of the involved distributions and with the concept of parameter independence of Heckerman et al.