# Learning Bayesian Network Structure from Massive Datasets: The "Sparse Candidate" Algorithm

arXiv: https://arxiv.org/abs/1301.6696 · HTML: https://mlsanity.com/paper/1301.6696/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2013.

## Built on by (most cited first, 22 of 22)

- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [A Survey on Causal Discovery Methods for I.I.D. and Time Series Data](https://mlsanity.com/paper/2303.15027/) (2023)
- [Efficient Bayesian network structure learning via local Markov boundary search](https://mlsanity.com/paper/2110.06082/) (2021)
- [Logical Entity Representation in Knowledge-Graphs for Differentiable Rule Learning](https://mlsanity.com/paper/2305.12738/) (2023)
- [Highly Efficient Structural Learning of Sparse Staged Trees](https://mlsanity.com/paper/2206.06970/) (2022)
- [Learning bounded-degree polytrees with known skeleton](https://mlsanity.com/paper/2310.06333/) (2023)
- [Partitioned hybrid learning of Bayesian network structures](https://mlsanity.com/paper/2103.12188/) (2021)
- [Optimal estimation of Gaussian (poly)trees](https://mlsanity.com/paper/2402.06380/) (2024)
- [Learning and interpreting asymmetry-labeled DAGs: a case study on COVID-19 fear](https://mlsanity.com/paper/2301.00629/) (2023)
- [How do some Bayesian Network machine learned graphs compare to causal knowledge?](https://mlsanity.com/paper/2101.10461/) (2021)
- [A Stochastic Variance-Reduced Coordinate Descent Algorithm for Learning Sparse Bayesian Network from Discrete High-Dimensional Data](https://mlsanity.com/paper/2108.09501/) (2021)
- [Learning Multitask Gaussian Bayesian Networks](https://mlsanity.com/paper/2205.05343/) (2022)
- [Distribution Learning Meets Graph Structure Sampling](https://mlsanity.com/paper/2405.07914/) (2024)
- [Learnability of Parameter-Bounded Bayes Nets](https://mlsanity.com/paper/2407.00927/) (2024)
- [Econometric vs. Causal Structure-Learning for Time-Series Policy Decisions: Evidence from the UK COVID-19 Policies](https://mlsanity.com/paper/2603.00041/) (2026)
- [KG-SoftMAP: Soft Knowledge-Graph Priors for Bayesian Network Structure Learning from Sparse Discrete Data](https://mlsanity.com/paper/2606.10358/) (2026)
- [Optimal Clustering with Dependent Costs in Bayesian Networks](https://mlsanity.com/paper/2308.03970/) (2023)
- [Exact discovery is polynomial for certain sparse causal Bayesian networks](https://mlsanity.com/paper/2406.15012/) (2024)
- [Scalable Structure Learning of Bayesian Networks by Learning Algorithm Ensembles](https://mlsanity.com/paper/2506.22848/) (2025)
- [Optimal structure learning and conditional independence testing](https://mlsanity.com/paper/2507.05689/) (2025)
- [Semi-overlapping Multi-bandit Best Arm Identification for Sequential Support Network Learning](https://mlsanity.com/paper/2512.24959/) (2025)
- [ABSOL: Aggregated Bayesian Subsampling Orchestrated with LLMs](https://mlsanity.com/paper/2609.15007/) (2026)

## Abstract (arXiv)

Learning Bayesian networks is often cast as an optimization problem, where the computational task is to find a structure that maximizes a statistically motivated score. By and large, existing learning tools address this optimization problem using standard heuristic search techniques. Since the search space is extremely large, such search procedures can spend most of the time examining candidates that are extremely unreasonable. This problem becomes critical when we deal with data sets that are large either in the number of instances, or the number of attributes. In this paper, we introduce an algorithm that achieves faster learning by restricting the search space. This iterative algorithm restricts the parents of each variable to belong to a small subset of candidates. We then search for a network that satisfies these constraints. The learned network is then used for selecting better candidates for the next iteration. We evaluate this algorithm both on synthetic and real-life data. Our results show that it is significantly faster than alternative search procedures without loss of quality in the learned structures.