Hypothesis testing for populations of networks

It has become an increasingly common practice in modern science and engineering to collect samples of multiple network data which a serves as basic object. The increasing prevalence calls for developments models theories that can deal with inference problems populations networks. In this work, we propose general procedure hypothesis testing networks particular, differentiating distributions two We consider very framework allows us perform test on large sparse Our contribution is two-fold: (1) statistics based the singular value generalized Wigner matrix. asymptotic null distribution shown follow Tracy–Widom number nodes tends infinity. also yields power guarantee tending one under alternative; (2) adapted change-point detection dynamic proven be consistent detecting change-points. addition theoretical guarantees, another appealing feature it provides principled simple method selecting threshold allowed vary time. Extensive simulation studies real analyses demonstrate superior performance our competitors.