Lee Kuang-Yao, Li Bing, Zhao Hongyu
Department of Biostatistics, Yale School of Public Health, 60 College Street, New Haven, Connecticut 06520, U.S.A.
Department of Statistics, Pennsylvania State University, 326 Thomas Building, University Park, Pennsylvania 16802, U.S.A.,
Biometrika. 2016 Sep;103(3):513-530. doi: 10.1093/biomet/asw028. Epub 2016 Aug 24.
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 independence, 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.
我们引入了一种加性偏相关算子，作为偏相关在非线性设置下的扩展，并使用它来开发一种用于非参数图形模型的新估计器。我们的图形模型基于加性条件独立性，这是一种统计关系，它捕捉了条件独立性的本质，而无需借助高维核来进行估计。加性偏相关算子完全刻画了加性条件独立性，并且在评估相互依赖性时具有将边际变化置于适当尺度上的额外优势，这导致更准确的统计推断。我们建立了所提出估计器的一致性。通过模拟实验和对DREAM4挑战数据集的分析，我们证明，在高斯或copula高斯假设不成立的情况下，我们的方法比现有方法表现更好，并且对我们的方法进行更合适的尺度调整会进一步提高其性能。
