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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 areinteresting or unexpected through maximization of a likelihood ratio statistic;in particular, nonparametric scan statistics (NPSSs) identify subgraphs with ahigher than expected proportion of individually significant nodes. However, weshow that recently proposed NPSS methods are miscalibrated, failing to accountfor the maximization of the statistic over the multiplicity of subgraphs. Thisresults in both reduced detection power for subtle signals, and low precisionof the detected subgraph even for stronger signals. Thus we develop a newstatistical approach to recalibrate NPSSs, correctly adjusting for multiplehypothesis testing and taking the underlying graph structure into account.While the recalibration, based on randomization testing, is computationallyexpensive, we propose both an efficient (approximate) algorithm and new,closed-form lower bounds (on the expected maximum proportion of significantnodes for subgraphs of a given size, under the null hypothesis of no anomalouspatterns). These advances, along with the integration of recent core-treedecomposition methods, enable CNSS to scale to large real-world graphs, withsubstantial improvement in the accuracy of detected subgraphs. Extensiveexperiments on both semi-synthetic and real-world datasets are demonstrated tovalidate the effectiveness of our proposed methods, in comparison withstate-of-the-art counterparts.

Calibrated Nonparametric Scan Statistics for Anomalous Pattern Detection in Graphs