On an additive partial correlation operator and nonparametric estimation of graphical models

Kuang-Yao Lee, Bing Li, Hongyu Zhao
2016 Biometrika  
We introduce an additive partial correlation operator as an extension of partial correlation to the nonlinear setting, and use it to develop a new estimator for nonparametric graphical models. Our graphical models are based on additive conditional independence, a statistical relation that captures the spirit of conditional independence without having to resort to high-dimensional kernels for its estimation. The additive partial correlation operator completely characterizes additive conditional
more » ... ndependence, and has the additional advantage of putting marginal variation on appropriate scales when evaluating interdependence, which leads to more accurate statistical inference. We establish the consistency of the proposed estimator. Through simulation experiments and analysis of the DREAM4 Challenge dataset, we demonstrate that our method performs better than existing methods in cases where the Gaussian or copula Gaussian assumption does not hold, and that a more appropriate scaling for our method further enhances its performance.
doi:10.1093/biomet/asw028 pmid:29422689 pmcid:PMC5793672 fatcat:4yllodfgzvanffj7dp5dmht4ny