# Bayesian Causal Inference with Gaussian Process Networks

arXiv: https://arxiv.org/abs/2402.00623 · HTML: https://mlsanity.com/paper/2402.00623/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 56 references that are in the map.
- First posted on arXiv 1 Feb 2024.

## Builds on (most cited first, 17 of 17)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Causality for Machine Learning](https://mlsanity.com/paper/1911.10500/) (2019)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributions](https://mlsanity.com/paper/1301.6697/) (2013)
- [Addendum on the scoring of Gaussian directed acyclic graphical models](https://mlsanity.com/paper/1402.6863/) (2014)
- [Partition MCMC for inference on acyclic digraphs](https://mlsanity.com/paper/1504.05006/) (2015)
- [Towards Scalable Bayesian Learning of Causal DAGs](https://mlsanity.com/paper/2010.00684/) (2020)
- [Efficient Sampling and Structure Learning of Bayesian Networks](https://mlsanity.com/paper/1803.07859/) (2018)
- [Estimating the effect of joint interventions from observational data in sparse high-dimensional settings](https://mlsanity.com/paper/1407.2451/) (2014)
- [Optimal experimental design via Bayesian optimization: active causal structure learning for Gaussian process networks](https://mlsanity.com/paper/1910.03962/) (2019)
- [Bayesian structure learning and sampling of Bayesian networks with the R package BiDAG](https://mlsanity.com/paper/2105.00488/) (2021)
- [Gaussian Process Networks](https://mlsanity.com/paper/1301.3857/) (2013)
- [A Bayesian Take on Gaussian Process Networks](https://mlsanity.com/paper/2306.11380/) (2023)
- [Marginal integration for nonparametric causal inference](https://mlsanity.com/paper/1405.1868/) (2014)
- [Weighted quantile estimators](https://mlsanity.com/paper/2304.07265/) (2023)

## Built on by (most cited first, 3 of 3)

- [Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learning](https://mlsanity.com/paper/2507.05526/) (2025)
- [Effective Bayesian Causal Inference via Structural Marginalisation and Autoregressive Orders](https://mlsanity.com/paper/2402.14781/) (2024)
- [Deep Gaussian Processes on Directed Acyclic Graphs](https://mlsanity.com/paper/2607.09645/) (2026)

## Abstract (arXiv)

Causal discovery and inference from observational data is an essential problem in statistics posing both modeling and computational challenges. These are typically addressed by imposing strict assumptions on the joint distribution such as linearity. We consider the problem of the Bayesian estimation of the effects of hypothetical interventions in the Gaussian Process Network (GPN) model, a flexible causal framework which allows describing the causal relationships nonparametrically. We detail how to perform causal inference on GPNs by simulating the effect of an intervention across the whole network and propagating the effect of the intervention on downstream variables. We further derive a simpler computational approximation by estimating the intervention distribution as a function of local variables only, modeling the conditional distributions via additive Gaussian processes. We extend both frameworks beyond the case of a known causal graph, incorporating uncertainty about the causal structure via Markov chain Monte Carlo methods. Simulation studies show that our approach is able to identify the effects of hypothetical interventions with non-Gaussian, non-linear observational data and accurately reflect the posterior uncertainty of the causal estimates. Finally we compare the results of our GPN-based causal inference approach to existing methods on a dataset of A.~thaliana gene expressions.