  Probabilistic graphical models are graphical representations of probability
distributions. Graphical models have applications in many fields including
biology, social sciences, linguistic, neuroscience. In this paper, we propose
directed acyclic graphs (DAGs) learning via bootstrap aggregating. The proposed
procedure is named as DAGBag. Specifically, an ensemble of DAGs is first
learned based on bootstrap resamples of the data and then an aggregated DAG is
derived by minimizing the overall distance to the entire ensemble. A family of
metrics based on the structural hamming distance is defined for the space of
DAGs (of a given node set) and is used for aggregation. Under the
high-dimensional-low-sample size setting, the graph learned on one data set
often has excessive number of false positive edges due to over-fitting of the
noise. Aggregation overcomes over-fitting through variance reduction and thus
greatly reduces false positives. We also develop an efficient implementation of
the hill climbing search algorithm of DAG learning which makes the proposed
method computationally competitive for the high-dimensional regime. The DAGBag
procedure is implemented in the R package dagbag.
