Reconstruction Of Networks With Binary-state Dynamics Via Generalized Statistical Inference

Many real systems can be represented by the complex networks in which nodes denote the units of the considered systems and the links connecting dif-ferent nodes represent the relationships between units,respectively.Studying these complex networks can help us better understand the real world.There-fore,more and more attention has been paid to the study of complex networks.However,the structure of many networks is often unknown,as a result,devel-oping methods on network reconstruction is particularly important.Network reconstruction mainly tries to find out the relationship bet.ween nodes and then infer the network structure from the dynamic characteristics of the nodes.Complex networks hosting binary-state dynamics can describe many phenomena in real life,so there are some methods for reconstructing networks using binary-state dynamics.However,they often hold two assump-tions:(1)require a priori knowledge about which state is the active state;(2)only one side of transition probability is utilized for network reconstruction.Many binary-state dynamics,such as cooperative/defective state in evolution-ary game model,the support/negative state of the viewpoint dynamics model,it is difficult t.o define which state is t,he act.ive state,what's more,both sides of the transition probability depend on the states of neighbors.For this situa-tion,if we only consider one side of transition probability,the reconstruction accuracy is greatly discounted because many data are not effect,ively used.By discarding the two hypotheses,this paper proposes a generalized EM algorith-m(abbreviated as GEM)to rec:onstruct a network with binary-state dynamics based on the statistical inference framework.The main contributions of this paper are as follows:1.This paper mainly proposes a generalized statistical inference method based on the assumption of a small amount of binary data to estimate the net-work topology.Different from the previous reconstruction methods that need to know the active state and predict the network topology with one-way tran-sition probability,the method in this paper is more general,we first propose a criterion to determine the category of one given binary-state dynamics.Then if the dynamics is the unidirectional dynamics,we can automatically identify the active state and reconstruct the network using the EM method.For the bidirectional dynamics,the GEM method proposed is used to reconstruction with the bidirectional transition probability.2.The simulation experiments are implemented on some empirical net-works and generated networks using six types of binary-state dynamical pro-cesses,and the results are compared with some previous methods.The results show that the generalized statistical inference met,hod significantly improves the reconstruction accuracy,and the noise is also considered,to validate the robustness of the method.