# Scalable Bayesian Network Structure Learning with Splines

arXiv: https://arxiv.org/abs/2110.14626 · HTML: https://mlsanity.com/paper/2110.14626/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 27 Oct 2021.

## Builds on (most cited first, 10 of 10)

- [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)
- [Learning Equivalence Classes of Bayesian Networks Structures](https://mlsanity.com/paper/1302.3566/) (2013)
- [Context-Specific Independence in Bayesian Networks](https://mlsanity.com/paper/1302.3562/) (2013)
- [Towards Scalable Bayesian Learning of Causal DAGs](https://mlsanity.com/paper/2010.00684/) (2020)
- [Theory Refinement on Bayesian Networks](https://mlsanity.com/paper/1303.5709/) (2013)
- [A Bayesian Approach to Learning Bayesian Networks with Local Structure](https://mlsanity.com/paper/1302.1528/) (2013)
- [Learning Bayesian Networks with Local Structure](https://mlsanity.com/paper/1302.3577/) (2013)
- [Advances in Bayesian Network Learning using Integer Programming](https://mlsanity.com/paper/1309.6825/) (2013)
- [A Score-and-Search Approach to Learning Bayesian Networks with Noisy-OR Relations](https://mlsanity.com/paper/2011.01444/) (2020)

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

- [A Bayesian Take on Gaussian Process Networks](https://mlsanity.com/paper/2306.11380/) (2023)
- [Learning Dynamic Bayesian Networks from Data: Foundations, First Principles and Numerical Comparisons](https://mlsanity.com/paper/2406.17585/) (2024)

## Abstract (arXiv)

The graph structure of a Bayesian network (BN) can be learned from data using the well-known score-and-search approach. Previous work has shown that incorporating structured representations of the conditional probability distributions (CPDs) into the score-and-search approach can improve the accuracy of the learned graph. In this paper, we present a novel approach capable of learning the graph of a BN and simultaneously modelling linear and non-linear local probabilistic relationships between variables. We achieve this by a combination of feature selection to reduce the search space for local relationships and extending the score-and-search approach to incorporate modelling the CPDs over variables as Multivariate Adaptive Regression Splines (MARS). MARS are polynomial regression models represented as piecewise spline functions. We show on a set of discrete and continuous benchmark instances that our proposed approach can improve the accuracy of the learned graph while scaling to instances with a large number of variables.