Abstract
Bayesian networks (BNs) provide a probabilistic, graphical framework for modeling high-dimensional joint distributions with complex correlation structures. BNs have wide applications in many disciplines, including biology, social science, finance and biomedical science. Despite extensive studies in the past, network structure learning from data is still a challenging open question in BN research. In this study, we present a sequential Monte Carlo (SMC)-based three-stage approach, GRowth-based Approach with Staged Pruning (GRASP). A double filtering strategy was first used for discovering the overall skeleton of the target BN. To search for the optimal network structures we designed an adaptive SMC (adSMC) algorithm to increase the quality and diversity of sampled networks which were further improved by a third stage to reclaim edges missed in the skeleton discovery step. GRASP gave very satisfactory results when tested on benchmark networks. Finally, BN structure learning using multiple types of genomics data illustrates GRASP’s potential in discovering novel biological relationships in integrative genomic studies.
Highlights
A Bayesian network (BN) is a graphical representation of the joint probability distribution of a set of variables
In the second stage, we developed an adaptive sequential Monte Carlo method to search the BN structure on the undirected network found in the first stage based on Bayesian information criterion (BIC) score
We developed a three-stage Bayesian network structure learning method, GRowth-based Approach with Staged Pruning (GRASP)
Summary
A Bayesian network (BN) is a graphical representation of the joint probability distribution of a set of variables (called nodes in the graph). A BN encodes conditional dependencies and independencies (CDIs) among variables into a directed acyclic graph (DAG). This DAG is called the structure of a BN. When the structure of a BN is given, the parameters that quantify the CDIs can be estimated from observed data. If neither the structure nor parameters are given, they can be inferred from observed data. We will be focusing on the structure estimation of a BN and its application in learning biological networks using heterogeneous genomics data
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