A network Lasso model for regression

Samples often are collected by a network in many modern applications, and the network structure information is potentially helpful in making regression predictions. However, most regression models assume the samples are independent, such as Lasso. Motivated by this, taking the network information into account, we propose a Network Lasso model for regression prediction in this paper. Specially, we consider the effect of the neighborhoods to each response and model each yi as a linear combination of the covariates xi, the connected neighbors yj, and an error term ϵi. The corresponding coefficients are referred to effect of node and neighborhoods, respectively. The consistency of the estimators are also established under the regimes where the neighborhoods effect coefficients are known and unknown, respectively. Finally, we evaluate the performance of the proposed model through a series of simulations and a latitude data example.