Network reconstruction based on structure energy

Fruitful research has been done for network reconstruction by taking sparsity or other similar statistical properties into consideration. By contrast, this paper sought to recover the network structure by means of a hybrid approach combining both sparsity and structure balance from a Bayesian perspective. This paper consider the situation where the state-space model is used to represent the structure information, in which, only a small fraction of input-output data can be obtained compared with the structure parameters to be identified. Both sparsity and structure balance are proposed to be structure potential terms of exponential random graph model(ERGM) in this paper. This paper simplify ERGM prior to make the MAP estimation to be easy enough yet capable of capturing sparsity and structure balance property of networks and the loss function with regulations is obtained. A heuristic relaxed form and a gradient based method are derived. This offer an alternative approach to deal with ERGM as the prior distribution of networks for network reconstruction problems. The effectiveness of the proposed method is demonstrated via simulation. Taken together, ERGM can provide new insights into designing case specific prior distribution of network structure for network reconstruction based on the Bayesian methods.