# Gaussian Process Networks

arXiv: https://arxiv.org/abs/1301.3857 · HTML: https://mlsanity.com/paper/1301.3857/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2013.

## Built on by (most cited first, 16 of 16)

- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [Active Bayesian Causal Inference](https://mlsanity.com/paper/2206.02063/) (2022)
- [Causal Entropy Optimization](https://mlsanity.com/paper/2208.10981/) (2022)
- [Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learning](https://mlsanity.com/paper/2507.05526/) (2025)
- [Bivariate Causal Discovery using Bayesian Model Selection](https://mlsanity.com/paper/2306.02931/) (2023)
- [Semiparametric Bayesian Networks](https://mlsanity.com/paper/2109.03008/) (2021)
- [Continuous Bayesian Model Selection for Multivariate Causal Discovery](https://mlsanity.com/paper/2411.10154/) (2024)
- [Boosting Synthetic Data Generation with Effective Nonlinear Causal Discovery](https://mlsanity.com/paper/2301.07427/) (2023)
- [A Bayesian Take on Gaussian Process Networks](https://mlsanity.com/paper/2306.11380/) (2023)
- [Bayesian Causal Inference with Gaussian Process Networks](https://mlsanity.com/paper/2402.00623/) (2024)
- [Optimal Kernel Choice for Score Function-based Causal Discovery](https://mlsanity.com/paper/2407.10132/) (2024)
- [Causal Identification with Additive Noise Models: Quantifying the Effect of Noise](https://mlsanity.com/paper/2110.08087/) (2021)
- [Graph Agnostic Causal Bayesian Optimisation](https://mlsanity.com/paper/2411.03028/) (2024)
- [The Effect of Noise Level on Causal Identification with Additive Noise Models](https://mlsanity.com/paper/2108.11320/) (2021)
- [Semi-parametric Expert Bayesian Network Learning with Gaussian Processes and Horseshoe Priors](https://mlsanity.com/paper/2401.16419/) (2024)
- [Bandwidth Selectors on Semiparametric Bayesian Networks](https://mlsanity.com/paper/2506.16844/) (2025)

## Abstract (arXiv)

In this paper we address the problem of learning the structure of a Bayesian network in domains with continuous variables. This task requires a procedure for comparing different candidate structures. In the Bayesian framework, this is done by evaluating the {em marginal likelihood/} of the data given a candidate structure. This term can be computed in closed-form for standard parametric families (e.g., Gaussians), and can be approximated, at some computational cost, for some semi-parametric families (e.g., mixtures of Gaussians). We present a new family of continuous variable probabilistic networks that are based on {em Gaussian Process/} priors. These priors are semi-parametric in nature and can learn almost arbitrary noisy functional relations. Using these priors, we can directly compute marginal likelihoods for structure learning. The resulting method can discover a wide range of functional dependencies in multivariate data. We develop the Bayesian score of Gaussian Process Networks and describe how to learn them from data. We present empirical results on artificial data as well as on real-life domains with non-linear dependencies.