Understanding the Effect of Bias in Deep Anomaly Detection

Anomaly detection presents a unique challenge in machine learning, due to the scarcity of labeled anomaly data. Recent work attempts to mitigate such problems by augmenting training of deep anomaly detection models with additional labeled anomaly samples. However, the labeled data often does not align with the target distribution and introduces harmful bias to the trained model. In this paper, we aim to understand the effect of a biased anomaly set on anomaly detection. We formally state the anomaly detection problem as a supervised learning task, and focus on the anomaly detector’s recall at a given false positive rate as the main performance metric. Given two different anomaly score functions, we formally define their difference in performance as the relative scoring bias of the anomaly detectors. Along this line, our work provides two key contributions. We establish the first finite sample rates for estimating the relative scoring bias for deep anomaly detection, and empirically validate our theoretical results on both synthetic and real-world datasets. We also provide extensive empirical study on how a biased training anomaly set affects the anomaly score function and therefore the detection performance on different anomaly classes. Our study demonstrates scenarios in which the biased anomaly set can be useful or problematic, and provides a solid benchmark for future research.