mlsanityData to 7 Oct 2026

Bayesian Network Learning via Topological Order

arXiv 1701.05654 ↗First posted 20 Jan 2017stat.ML cs.DScited by 14

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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.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). First posted on arXiv 20 Jan 2017.

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Citing papers per year: 2021: 3; 2022: 2; 2023: 5; 2024: 2; 2025: 1; 2026: 1.

14 papers.

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  1. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 209
  2. 2022Diffusion Models for Causal Discovery via Topological Orderingcited by 64
  3. 2022Differentiable DAG Samplingcited by 46
  4. 2023Optimizing NOTEARS Objectives via Topological Swapscited by 17
  5. 2021Integer Programming for Causal Structure Learning in the Presence of Latent Variablescited by 14
  6. 2023CoLiDE: Concomitant Linear DAG Estimationcited by 12
  7. 2023Global Optimality in Bivariate Gradient-based DAG Learningcited by 10
  8. 2023Order-based Structure Learning with Normalizing Flowscited by 4
  9. 2024Integer Programming for Learning Directed Acyclic Graphs from Non-identifiable Gaussian Modelscited by 4
  10. 2021Learning Large DAGs by Combining Continuous Optimization and Feedback Arc Set Heuristicscited by 2
  11. 2023Hierarchical Topological Ordering with Conditional Independence Test for Limited Time Seriescited by 1
  12. 2025Causal Ordering for Structure Learning from Time Seriescited by 1
2 more
  1. 2024Learning Dynamic Bayesian Networks from Data: Foundations, First Principles and Numerical Comparisonscited by 0
  2. 2026Coordinate Optimality Reformulation for Mixed-Integer Convex Programs with Indicatorscited by 0