Learning Nonparametric Forest Graphical Models with Prior Information
This work provides an incremental improvement for researchers estimating graphical models with prior knowledge, particularly in scale-free or multiple-graph settings.
The authors developed a framework for incorporating prior information into nonparametric forest graphical models, avoiding distributional assumptions by restricting graphs to forests. Their methods outperformed competing parametric approaches in simulations and improved predictive power and interpretability in real datasets.
We present a framework for incorporating prior information into nonparametric estimation of graphical models. To avoid distributional assumptions, we restrict the graph to be a forest and build on the work of forest density estimation (FDE). We reformulate the FDE approach from a Bayesian perspective, and introduce prior distributions on the graphs. As two concrete examples, we apply this framework to estimating scale-free graphs and learning multiple graphs with similar structures. The resulting algorithms are equivalent to finding a maximum spanning tree of a weighted graph with a penalty term on the connectivity pattern of the graph. We solve the optimization problem via a minorize-maximization procedure with Kruskal's algorithm. Simulations show that the proposed methods outperform competing parametric methods, and are robust to the true data distribution. They also lead to improvement in predictive power and interpretability in two real data sets.