Robustness of Network Structure Identification

Abstract

In this chapter, we discuss robustness of network structure identification algorithms. We understand robustness of identification algorithm as the stability of the risk function with respect to the distribution of the vector X from some class of distributions (distribution free property). We show that popular identification algorithms based on sample Pearson correlations are not robust in the class of elliptical distributions. To overcome this issue, we consider the sign similarity network, introduce a new class of network structure identification algorithms, and prove its robustness in the class of elliptical distributions. We show how to use these algorithms to construct robust network structure identification algorithms in other correlation networks.