A double regression method for graphical modeling of high-dimensional nonlinear and non-Gaussian data

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.

Keywords

conditional independence tests, directed acyclic graph, dimension reduction, Markov blanket, Markov network

2010 Mathematics Subject Classification

Primary 62H20, 62J02. Secondary 62P10.

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Received 5 October 2021

Accepted 2 September 2022

Published 19 July 2024