Greedy learning of graph connectivity from partially-observed cascade samples

Abstract

Graph learning is an inference problem of estimating the nodes’ connectivity from a collection of epidemic cascades, with many useful applications in the areas of in online/offline social networks, p2p networks, computer security, and epidemiology. We consider a case when the information of cascade samples are only partially observed under the IC (Independent Cascade) epidemic model, where our interest is to compute the sample complexity, i.e., a required number of cascade samples to achieve a given target inference accuracy. We first provide a fundamental lower bound on the sample complexity. Then, motivated by the fact that the famous Maximum Likelihood Estimator (MLE) is computationally intractable, we propose a greedy heuristic that works based on counting the estimated number of possible activation path, which we call counting of virtual activation paths, where the key strength lies in having much smaller computational complexity than the algorithm based on the approximation of MLE. We analyze the sample complexity of our greedy heuristic, which is close to optimal for some graphs where activation propagates ceaselessly. We evaluate the performance of our algorithm over various types of graph topologies.