Network Varying Coefficient Model

We propose a novel network-varying coefficient model that extends traditional varying coefficient models to accommodate network data. The main idea is to model the regression coefficients as the functions of the latent “locations” of network nodes that drive formation of the network. To estimate the model, we identify the latent “locations” via the latent space model and then develop an iterative projected gradient descent algorithm by optimizing the network parameters and regression coefficients alternately. The non-asymptotic bounds of the estimated coefficient matrix are obtained. In addition, a Bayesian information criterion is proposed to select the dimension of the latent space. Moreover, we employ a penalized method to select covariates with varying coefficients that are significant to the response variable, and demonstrate the theoretical properties of selection. The utility of the proposed model is illustrated via simulation studies and a real-world application in the field of finance by analyzing the relationship between stock returns and their corresponding financial ratios from a network perspective.