Learning Moral Graphs in Construction of High-Dimensional Bayesian Networks for Mixed Data

• Activity Number: 467 - Modeling, Design Strategies and Assessment of Biomarkers
• Type: Contributed
• Date/Time: Wednesday, July 31, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Biopharmaceutical Section
• Author(s): Bochao Jia* and Suwa Xu and Faming Liang
• Companies: Eli Lilly and Company and University of Florida and Purdue University
• Keywords: Bayesian Network; Conditional Independence Tests; Graphical Model; Faithfulness Markov Blanket; Moral Graph

Abstract

Bayesian networks have been widely used in many scientific fields for describing the conditional independence relationships for a large set of random variables. This paper proposes a novel algorithm, the so-called p-learning algorithm, for learning the moral graph for high-dimensional Bayesian networks. The moral graph is a Markov network representation of the Bayesian network and also the key to construction of the Bayesian network. The consistency of the p-learning algorithm is justified under the small-n-large-p scenario. The numerical results indicate that the p-learning algorithm significantly outperforms the existing ones, such as the PC, grow-shrink, incremental association, semi-interleaved hiton, hill-climbing, and max-min hill-climbing. Under the sparsity assumption, the p-learning algorithm has a computational complexity of O(p2) even in the worst case, while the existing algorithms has a computational complexity of O(p3) in the worst case. The real example illustrated that our proposed method can identify some key driven genes and high impact mutations in the breast cancer genomics network.