# A Stochastic Variance-Reduced Coordinate Descent Algorithm for Learning Sparse Bayesian Network from Discrete High-Dimensional Data

arXiv: https://arxiv.org/abs/2108.09501 · HTML: https://mlsanity.com/paper/2108.09501/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 56 references that are in the map.
- First posted on arXiv 21 Aug 2021.

## Builds on (most cited first, 11 of 11)

- [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)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [A Survey of Optimization Methods from a Machine Learning Perspective](https://mlsanity.com/paper/1906.06821/) (2019)
- [DAGs with No Curl: An Efficient DAG Structure Learning Approach](https://mlsanity.com/paper/2106.07197/) (2021)
- [Concave Penalized Estimation of Sparse Gaussian Bayesian Networks](https://mlsanity.com/paper/1401.0852/) (2014)
- [Learning Bayesian Network Structure from Massive Datasets: The "Sparse Candidate" Algorithm](https://mlsanity.com/paper/1301.6696/) (2013)
- [MURANA: A Generic Framework for Stochastic Variance-Reduced Optimization](https://mlsanity.com/paper/2106.03056/) (2021)
- [Penalized Estimation of Directed Acyclic Graphs From Discrete Data](https://mlsanity.com/paper/1403.2310/) (2014)
- [Learning Large-Scale Bayesian Networks with the sparsebn Package](https://mlsanity.com/paper/1703.04025/) (2017)

## Built on by (most cited first, 1 of 1)

- [Learning and interpreting asymmetry-labeled DAGs: a case study on COVID-19 fear](https://mlsanity.com/paper/2301.00629/) (2023)

## Abstract (arXiv)

This paper addresses the problem of learning a sparse structure Bayesian network from high-dimensional discrete data. Compared to continuous Bayesian networks, learning a discrete Bayesian network is a challenging problem due to the large parameter space. Although many approaches have been developed for learning continuous Bayesian networks, few approaches have been proposed for the discrete ones. In this paper, we address learning Bayesian networks as an optimization problem and propose a score function which guarantees the learnt structure to be a sparse directed acyclic graph. Besides, we implement a block-wised stochastic coordinate descent algorithm to optimize the score function. Specifically, we use a variance reducing method in our optimization algorithm to make the algorithm work efficiently for high-dimensional data. The proposed approach is applied to synthetic data from well-known benchmark networks. The quality, scalability, and robustness of the constructed network are measured. Compared to some competitive approaches, the results reveal that our algorithm outperforms some of the well-known proposed methods.