Calibrated Nonparametric Scan Statistics for Anomalous Pattern Detection in Graphs

TL;DR

This paper introduces the calibrated nonparametric scan statistic (CNSS), a new method for more accurate detection of anomalous subgraphs in large graphs by correcting calibration issues in existing methods and improving scalability.

Contribution

The paper develops a recalibration technique for nonparametric scan statistics, including efficient algorithms and bounds, enhancing detection accuracy and scalability in large-scale graph anomaly detection.

Findings

CNSS outperforms existing methods in accuracy on real-world datasets.

Recalibration improves detection power for subtle signals.

Proposed algorithms scale efficiently to large graphs.

Abstract

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