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

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 p-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 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 have a computational complexity of O(p3) in the worst case.

Learning gene regulatory networks from next generation sequencing data.

In recent years, next generation sequencing (NGS) has gradually replaced microarray as the major platform in measuring gene expressions. Compared to microarray, NGS has many advantages, such as less noise and higher throughput. However, the discreteness of NGS data also challenges the existing statistical methodology. In particular, there still lacks an appropriate statistical method for reconstructing gene regulatory networks using NGS data in the literature. The existing local Poisson graphical model method is not consistent and can only infer certain local structures of the network. In this article, we propose a random effect model-based transformation to continuize NGS data and then we transform the continuized data to Gaussian via a semiparametric transformation and apply an equivalent partial correlation selection method to reconstruct gene regulatory networks. The proposed method is consistent. The numerical results indicate that the proposed method can lead to much more accurate inference of gene regulatory networks than the local Poisson graphical model and other existing methods. The proposed data-continuized transformation fills the theoretical gap for how to transform discrete data to continuous data and facilitates NGS data analysis. The proposed data-continuized transformation also makes it feasible to integrate different types of data, such as microarray and RNA-seq data, in reconstruction of gene regulatory networks.