  Diffusion source identification on networks is a problem of fundamental
importance in a broad class of applications, including rumor controlling and
virus identification. Though this problem has received significant recent
attention, most studies have focused only on very restrictive settings and lack
theoretical guarantees for more realistic networks. We introduce a statistical
framework for the study of diffusion source identification and develop a
confidence set inference approach inspired by hypothesis testing. Our method
efficiently produces a small subset of nodes, which provably covers the source
node with any pre-specified confidence level without restrictive assumptions on
network structures. Moreover, we propose multiple Monte Carlo strategies for
the inference procedure based on network topology and the probabilistic
properties that significantly improve the scalability. To our knowledge, this
is the first diffusion source identification method with a practically useful
theoretical guarantee on general networks. We demonstrate our approach via
extensive synthetic experiments on well-known random network models and a
mobility network between cities concerning the COVID-19 spreading.
