论文标题
高维非线性和非高斯数据的图形建模的双回归方法
A Double Regression Method for Graphical Modeling of High-dimensional Nonlinear and Non-Gaussian Data
论文作者
论文摘要
长期以来，在统计数据中研究了图形模型，作为推断大量随机变量之间有条件独立关系的工具。图形建模中最现有的作品集中在数据是高斯或混合的情况下，并且变量是线性依赖的。在本文中，我们提出了一种在高维非线性和非高斯环境下学习图形模型的双回归方法，并证明所提出的方法在轻度条件下是一致的。该方法通过执行一系列非参数条件独立性测试来起作用。通过双重回归程序可以减少每个测试的调节集，在该过程中，可以采用无模型的独立性筛选程序或稀疏的深神经网络。数值结果表明，该提出的方法适用于高维非线性和非高斯数据。
Graphical models have long been studied in statistics as a tool for inferring conditional independence relationships among a large set of random variables. The most existing works in graphical modeling focus on the cases that the data are Gaussian or mixed and the variables are linearly dependent. In this paper, we propose a double regression method for learning graphical models under the high-dimensional nonlinear and non-Gaussian setting, and prove that the proposed method is consistent under mild conditions. The proposed method works by performing a series of nonparametric conditional independence tests. The conditioning set of each test is reduced via a double regression procedure where a model-free sure independence screening procedure or a sparse deep neural network can be employed. The numerical results indicate that the proposed method works well for high-dimensional nonlinear and non-Gaussian data.
