  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.
