# A Bayesian Take on Gaussian Process Networks

arXiv: https://arxiv.org/abs/2306.11380 · HTML: https://mlsanity.com/paper/2306.11380/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 52 references that are in the map.
- First posted on arXiv 20 Jun 2023.

## Builds on (most cited first, 18 of 18)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [Structure Discovery in Nonparametric Regression through Compositional Kernel Search](https://mlsanity.com/paper/1302.4922/) (2013)
- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [Learning Gaussian Networks](https://mlsanity.com/paper/1302.6808/) (2013)
- [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)
- [Data Analysis with Bayesian Networks: A Bootstrap Approach](https://mlsanity.com/paper/1301.6695/) (2013)
- [Efficient Sampling and Structure Learning of Bayesian Networks](https://mlsanity.com/paper/1803.07859/) (2018)
- [Learning Bayesian Networks: A Unification for Discrete and Gaussian Domains](https://mlsanity.com/paper/1302.4957/) (2013)
- [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)
- [Scalable Bayesian Network Structure Learning with Splines](https://mlsanity.com/paper/2110.14626/) (2021)
- [The Dual PC Algorithm and the Role of Gaussianity for Structure Learning of Bayesian Networks](https://mlsanity.com/paper/2112.09036/) (2021)

## Built on by (most cited first, 4 of 4)

- [Effective Bayesian Causal Inference via Structural Marginalisation and Autoregressive Orders](https://mlsanity.com/paper/2402.14781/) (2024)
- [Bayesian Causal Inference with Gaussian Process Networks](https://mlsanity.com/paper/2402.00623/) (2024)
- [Graph Agnostic Causal Bayesian Optimisation](https://mlsanity.com/paper/2411.03028/) (2024)
- [Interpretable Causal Discovery via Causal-Effect Constraints](https://mlsanity.com/paper/2608.12640/) (2026)

## Abstract (arXiv)

Gaussian Process Networks (GPNs) are a class of directed graphical models which employ Gaussian processes as priors for the conditional expectation of each variable given its parents in the network. The model allows the description of continuous joint distributions in a compact but flexible manner with minimal parametric assumptions on the dependencies between variables. Bayesian structure learning of GPNs requires computing the posterior over graphs of the network and is computationally infeasible even in low dimensions. This work implements Monte Carlo and Markov Chain Monte Carlo methods to sample from the posterior distribution of network structures. As such, the approach follows the Bayesian paradigm, comparing models via their marginal likelihood and computing the posterior probability of the GPN features. Simulation studies show that our method outperforms state-of-the-art algorithms in recovering the graphical structure of the network and provides an accurate approximation of its posterior distribution.