Learning Nonparametric Forest Graphical Models with Prior Information

TL;DR

This paper introduces a Bayesian framework for nonparametric forest graphical models that incorporate prior information, improving estimation accuracy and interpretability without assuming specific data distributions.

Contribution

It develops a novel Bayesian approach to nonparametric forest graphical models, enabling the integration of prior knowledge and application to scale-free and multi-graph estimation.

Findings

Outperforms parametric methods in simulations

Robust to true data distribution variations

Enhances predictive power and interpretability

Abstract

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.