Bayesian Network Learning via Topological Order
This work addresses optimization challenges in Bayesian network learning for bioinformatics, but it is incremental as it builds on existing methods with specific improvements.
The authors tackled the problem of learning Bayesian networks by proposing a mixed integer programming model and iterative algorithms based on topological orders to reduce constraints and improve efficiency, achieving computational gains in experiments for Gaussian Bayesian network learning with applications in gene network inference.
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.