# An Asymptotically Optimal Coordinate Descent Algorithm for Learning Bayesian Networks from Gaussian Models

arXiv: https://arxiv.org/abs/2408.11977 · HTML: https://mlsanity.com/paper/2408.11977/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 21 Aug 2024.

## Builds on (most cited first, 13 of 13)

- [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)
- [On Causal Discovery with Equal Variance Assumption](https://mlsanity.com/paper/1807.03419/) (2018)
- [Fast Best Subset Selection: Coordinate Descent and Local Combinatorial Optimization Algorithms](https://mlsanity.com/paper/1803.01454/) (2018)
- [High-dimensional consistency in score-based and hybrid structure learning](https://mlsanity.com/paper/1507.02608/) (2015)
- [Concave Penalized Estimation of Sparse Gaussian Bayesian Networks](https://mlsanity.com/paper/1401.0852/) (2014)
- [Integer Programming for Learning Directed Acyclic Graphs from Continuous Data](https://mlsanity.com/paper/1904.10574/) (2019)
- [The Causal Chambers: Real Physical Systems as a Testbed for AI Methodology](https://mlsanity.com/paper/2404.11341/) (2024)
- [Learning Large-Scale Bayesian Networks with the sparsebn Package](https://mlsanity.com/paper/1703.04025/) (2017)
- [Optimizing regularized Cholesky score for order-based learning of Bayesian networks](https://mlsanity.com/paper/1904.12360/) (2019)
- [Consistent Second-Order Conic Integer Programming for Learning Bayesian Networks](https://mlsanity.com/paper/2005.14346/) (2020)
- [Sparse Gaussian Graphical Models with Discrete Optimization: Computational and Statistical Perspectives](https://mlsanity.com/paper/2307.09366/) (2023)
- [Integer Programming for Learning Directed Acyclic Graphs from Non-identifiable Gaussian Models](https://mlsanity.com/paper/2404.12592/) (2024)

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

- [Coordinate Optimality Reformulation for Mixed-Integer Convex Programs with Indicators](https://mlsanity.com/paper/2608.01385/) (2026)

## Abstract (arXiv)

This paper studies the problem of learning Bayesian networks from continuous observational data, generated according to a linear Gaussian structural equation model. We consider an ℓ0-penalized maximum likelihood estimator for this problem which is known to have favorable statistical properties but is computationally challenging to solve, especially for medium-sized Bayesian networks. We propose a new coordinate descent algorithm to approximate this estimator and prove several remarkable properties of our procedure: the algorithm converges to a coordinate-wise minimum, and despite the non-convexity of the loss function, as the sample size tends to infinity, the objective value of the coordinate descent solution converges to the optimal objective value of the ℓ0-penalized maximum likelihood estimator. Finite-sample statistical consistency guarantees are also established. To the best of our knowledge, our proposal is the first coordinate descent procedure endowed with optimality and statistical guarantees in the context of learning Bayesian networks. Numerical experiments on synthetic and real data demonstrate that our coordinate descent method can obtain near-optimal solutions while being scalable.