# Bayesian Network Learning via Topological Order

arXiv: https://arxiv.org/abs/1701.05654 · HTML: https://mlsanity.com/paper/1701.05654/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jan 2017.

## Built on by (most cited first, 14 of 14)

- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Diffusion Models for Causal Discovery via Topological Ordering](https://mlsanity.com/paper/2210.06201/) (2022)
- [Differentiable DAG Sampling](https://mlsanity.com/paper/2203.08509/) (2022)
- [Optimizing NOTEARS Objectives via Topological Swaps](https://mlsanity.com/paper/2305.17277/) (2023)
- [Integer Programming for Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2102.03129/) (2021)
- [CoLiDE: Concomitant Linear DAG Estimation](https://mlsanity.com/paper/2310.02895/) (2023)
- [Global Optimality in Bivariate Gradient-based DAG Learning](https://mlsanity.com/paper/2306.17378/) (2023)
- [Order-based Structure Learning with Normalizing Flows](https://mlsanity.com/paper/2308.07480/) (2023)
- [Integer Programming for Learning Directed Acyclic Graphs from Non-identifiable Gaussian Models](https://mlsanity.com/paper/2404.12592/) (2024)
- [Learning Large DAGs by Combining Continuous Optimization and Feedback Arc Set Heuristics](https://mlsanity.com/paper/2107.00571/) (2021)
- [Causal Ordering for Structure Learning from Time Series](https://mlsanity.com/paper/2510.24639/) (2025)
- [Hierarchical Topological Ordering with Conditional Independence Test for Limited Time Series](https://mlsanity.com/paper/2308.08148/) (2023)
- [Learning Dynamic Bayesian Networks from Data: Foundations, First Principles and Numerical Comparisons](https://mlsanity.com/paper/2406.17585/) (2024)
- [Coordinate Optimality Reformulation for Mixed-Integer Convex Programs with Indicators](https://mlsanity.com/paper/2608.01385/) (2026)

## Abstract (arXiv)

We propose a mixed integer programming (MIP) model and iterative algorithms based on topological orders to solve optimization problems with acyclic constraints on a directed graph. The proposed MIP model has a significantly lower number of constraints compared to popular MIP models based on cycle elimination constraints and triangular inequalities. The proposed iterative algorithms use gradient descent and iterative reordering approaches, respectively, for searching topological orders. A computational experiment is presented for the Gaussian Bayesian network learning problem, an optimization problem minimizing the sum of squared errors of regression models with L1 penalty over a feature network with application of gene network inference in bioinformatics.