Learning Nonparametric Forest Graphical Models with Prior Information

Yuancheng Zhu, Zhe Liu, Siqi Sun
Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:672-680, 2017.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v54-zhu17a, title = {{Learning Nonparametric Forest Graphical Models with Prior Information}}, author = {Zhu, Yuancheng and Liu, Zhe and Sun, Siqi}, booktitle = {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics}, pages = {672--680}, year = {2017}, editor = {Singh, Aarti and Zhu, Jerry}, volume = {54}, series = {Proceedings of Machine Learning Research}, month = {20--22 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v54/zhu17a/zhu17a.pdf}, url = {https://proceedings.mlr.press/v54/zhu17a.html}, 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.} }
Endnote
%0 Conference Paper %T Learning Nonparametric Forest Graphical Models with Prior Information %A Yuancheng Zhu %A Zhe Liu %A Siqi Sun %B Proceedings of the 20th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2017 %E Aarti Singh %E Jerry Zhu %F pmlr-v54-zhu17a %I PMLR %P 672--680 %U https://proceedings.mlr.press/v54/zhu17a.html %V 54 %X 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.
APA
Zhu, Y., Liu, Z. & Sun, S.. (2017). Learning Nonparametric Forest Graphical Models with Prior Information. Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 54:672-680 Available from https://proceedings.mlr.press/v54/zhu17a.html.

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