We present a novel bi-objective approach to address the data-driven learning problem of Bayesian networks. Both the log-likelihood and the complexity of each candidate Bayesian network are considered as objectives to be optimized by our proposed algorithm named Nondominated Sorting Genetic Algorithm for learning Bayesian networks (NS2BN) which is based on the well-known NSGA-II algorithm. The core idea is to reduce the implicit selection bias-variance decomposition while identifying a set of competitive models using both objectives. Numerical results suggest that, in stark contrast to the single-objective approach, our bi-objective approach is useful to find competitive Bayesian networks especially in the complexity. Furthermore, our approach presents the end user with a set of solutions by showing different Bayesian network and their respective MDL and classification accuracy results.
Discussion of “Data-driven confounder selection via Markov and Bayesian networks” by Häggström