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

Journal: Neural computation
Published Date:

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 letter proposes a novel algorithm, the so-called -learning algorithm, for learning moral graphs 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 for constraint-based algorithms. The consistency of the -learning algorithm is justified under the small-, large- scenario. The numerical results indicate that the -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 -learning algorithm has a computational complexity of even in the worst case, while the existing algorithms have a computational complexity of in the worst case.

Authors

  • Suwa Xu
    Department of Biostatistics, University of Florida, Gainesville, FL 32611, U.S.A. suwaxu@ufl.edu.
  • Bochao Jia
    Lilly Corporate Center, Eli Lilly and Company, Indianapolis, IN 46285, U.S.A. jia_bochao@lilly.com.
  • Faming Liang
    Department of Statistics, Purdue University, West Lafayette, IN 47906, U.S.A. fmliang@purdue.edu.