Calibrated Nonparametric Scan Statistics for Anomalous Pattern Detection in Graphs

We propose a new approach, the calibrated nonparametric scan statistic (CNSS), for more accurate detection of anomalous patterns in large-scale, real-world graphs. Scan statistics identify connected subgraphs that are interesting or unexpected through maximization likelihood ratio statistic; particular, (NPSSs) with higher than expected proportion individually significant nodes. However, we show recently proposed NPSS methods miscalibrated, failing to account over multiplicity subgraphs. This results both reduced power subtle signals, and low precision detected subgraph even stronger signals. Thus develop statistical approach recalibrate NPSSs, correctly adjusting multiple hypothesis testing taking underlying graph structure into account. While recalibration, based on randomization testing, is computationally expensive, an efficient (approximate) algorithm new, closed-form lower bounds (on maximum nodes given size, under null no patterns). These advances, along integration recent core-tree decomposition methods, enable CNSS scale large graphs, substantial improvement accuracy Extensive experiments semi-synthetic datasets demonstrated validate effectiveness our comparison state-of-the-art counterparts.