SparsityBoost: A New Scoring Function for Learning Bayesian Network Structure
This work addresses structure learning in Bayesian networks, offering a computationally efficient method for statisticians and machine learning practitioners, but it appears incremental as it builds on existing scoring and search approaches.
The authors tackled the problem of learning Bayesian network structures by introducing a new consistent scoring function with a data-dependent complexity penalty, which becomes computationally easier to maximize as data increases. They proved polynomial sample complexity for correct structure learning and demonstrated effectiveness with linear programming relaxation.
We give a new consistent scoring function for structure learning of Bayesian networks. In contrast to traditional approaches to scorebased structure learning, such as BDeu or MDL, the complexity penalty that we propose is data-dependent and is given by the probability that a conditional independence test correctly shows that an edge cannot exist. What really distinguishes this new scoring function from earlier work is that it has the property of becoming computationally easier to maximize as the amount of data increases. We prove a polynomial sample complexity result, showing that maximizing this score is guaranteed to correctly learn a structure with no false edges and a distribution close to the generating distribution, whenever there exists a Bayesian network which is a perfect map for the data generating distribution. Although the new score can be used with any search algorithm, we give empirical results showing that it is particularly effective when used together with a linear programming relaxation approach to Bayesian network structure learning.