Near-optimal and computationally efficient detectors for weak and sparse graph-structured patterns

In this paper, we review our recent work on detecting weak patterns that are sparse and localized on a graph. This problem is relevant to many applications including detecting anomalies in sensor and computer networks, brain activity, co-expressions in gene networks, disease outbreaks etc. We characterize such a class of weak and sparse graph-structured patterns by small subsets of weakly activated nodes with a low cut in an underlying known graph. On one hand, the combinatorial nature of this class renders traditional detectors such as GLRT (aka scan statistic) computationally intractable for general graphs. On the other hand, attempts to develop feasible detectors such as fast subset scanning or averaging/thresholding sacrifice statistical efficiency. We describe and compare three detectors for weak graph-structured patterns that are developed using tools from graph theory, optimization and machine learning. These detectors are computationally efficient, applicable to graphs and patterns with general structures and come with precise theoretical guarantees, often achieving near-optimal statistical performance.