Title: Bayesian Network Learning via Topological Order,
Abstract: 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.