Hierarchical Heavy Hitter Detection Under Unknown Models

We consider the problem of detecting heavy hitters and hierarchical heavy hitters among a large number of traffic flows modeled as random processes with unknown and potentially heavy-tailed distributions. The objective is an active inference strategy that determines, sequentially, which aggregated flow on the IP-prefix tree to probe in order to minimize the sample complexity under a reliability constraint. We propose an active inference strategy that induces a biased random walk on the flow aggregation tree based on confidence bounds of sample statistics. We then establish its order optimality in terms of both the size of the search space (i.e., the number of traffic flows) and the reliability requirement. The result also finds applications in noisy group testing and adaptive sampling with noisy response.