  In this work, we consider to improve the model estimation efficiency by
aggregating the neighbors' information as well as identify the subgroup
membership for each node in the network. A tree-based $l_1$ penalty is proposed
to save the computation and communication cost. We design a decentralized
generalized alternating direction method of multiplier algorithm for solving
the objective function in parallel. The theoretical properties are derived to
guarantee both the model consistency and the algorithm convergence. Thorough
numerical experiments are also conducted to back up our theory, which also show
that our approach outperforms in the aspects of the estimation accuracy,
computation speed and communication cost.
