A0793
Title: Assessing the explanatory power of high-dimensional node-level covariates on network structure
Authors: Alexander Fuchs-Kreiss - Leipzig University (Germany) [presenting]
Keith Levin - University of Wisconsin (United States)
Abstract: The purpose is to consider the problem of selecting from a high-dimensional set of covariates those that are explanatory of an observed network. Specifically, a network comprising vertices and undirected links is observed between them. In addition, for each vertex, a high-dimensional vector of covariates is observed (its dimension can exceed the number of vertices). To assess which of these covariates are correlated with the network structure, it is assumed that the network is generated by a random dot product graph (RDPG), and the aim is to understand if some covariates are related to the latent positions in the RDPG. This is achieved in three ways. Firstly, a model is proposed, and LASSO estimation is used. The unidentifiability in the RDPG translates to a group LASSO penalty. In a second approach, canonical correlation analysis (CCA) is used to quantify the strength of the relation between the latent positions and the covariates. Since the latent positions are unobserved, both methods are applied to the estimated latent positions. Thirdly, as an alternative, CCA is studied between the covariates and the rows of the adjacency matrix directly. This avoids the need for latent position estimation. For all the methods, the convergence of the estimators is rigorously shown. In a simulation study, it is shown that permutation tests based on the methods have good power in detecting relevant covariates from a high-dimensional set of covariates.
