Optimal Network-Guided Covariate Selection for High-Dimensional Data Integration

Modern data often arise with multiple modalities. For example, covariates and a network are observed on the same subjects, and both contain useful information. Effectively integrating these modalities is important and challenging, especially when the response is unavailable. We study the fundamental covariate selection problem for high-dimensional data by leveraging network information.We propose the Network-Guided Covariate Selection (NGCS) algorithm. NGCS exploits the spectral structure of the network to construct a network-guided screening statistic, and employs data-driven Higher Criticism Thresholding for covariate recovery. We establish consistency guarantees for NGCS under general networks. In particular, under two commonly used network models, we relate the projected signal strength to the individual signal strength, and demonstrate that NGCS is optimal for covariate selection. It could achieve the same rate as supervised learning.We further consider a two-study setting for downstream applications, where the network is observed only in Study 1. For clustering and regression, we propose NG-clu and NG-reg algorithms. NG-clu accurately clusters all subjects, while NG-reg improves prediction by using the post-selection covariate matrix. Experiments on synthetic and real datasets demonstrate the robustness and superior performance of our algorithms across various network models, noise distributions, and signal strengths.