Leave-One-Out-, Bootstrap- and Cross-Conformal Anomaly Detectors (2402.16388v3)

Abstract: The requirement of uncertainty quantification for anomaly detection systems has become increasingly important. In this context, effectively controlling Type I error rates ($\alpha$) without compromising the statistical power ($1-\beta$) of these systems can build trust and reduce costs related to false discoveries. The field of conformal anomaly detection emerges as a promising approach for providing respective statistical guarantees by model calibration. However, the dependency on calibration data poses practical limitations - especially within low-data regimes. In this work, we formally define and evaluate leave-one-out-, bootstrap-, and cross-conformal methods for anomaly detection, incrementing on methods from the field of conformal prediction. Looking beyond the classical inductive conformal anomaly detection, we demonstrate that derived methods for calculating resampling-conformal $p$-values strike a practical compromise between statistical efficiency (full-conformal) and computational efficiency (split-conformal) as they make more efficient use of available data. We validate derived methods and quantify their improvements for a range of one-class classifiers and datasets.

• The paper introduces cross-conformal methods that balance statistical guarantees with computational efficiency, improving anomaly detection reliability.
• It demonstrates empirically that these methods achieve superior FDR control and higher statistical power compared to traditional split-conformal approaches.
• Results highlight enhanced model stability and sensitivity, offering practical benefits for critical domains in cybersecurity, healthcare, and finance.

Extending Conformal Prediction to Enhance Anomaly Detection Systems with Cross-Conformal Methods

Introduction to Cross-Conformal Anomaly Detection

Anomaly detection continues to be an essential area of focus across various industries, including cybersecurity, healthcare, and finance, among others. As the demand for trustworthy and explainable machine learning systems grows, so does the need for robust anomaly detection systems that incorporate uncertainty quantification. Recent advancements have been made by extending the capabilities of conformal prediction techniques to the field of anomaly detection, leading to the development of cross-conformal anomaly detection methods. This paper provides a comprehensive examination of these methods, comparing them with traditional split-conformal approaches in terms of False Discovery Rate (FDR) control and statistical power.

Cross-Conformal Methods for Anomaly Detection

Conformal prediction techniques offer a promising solution by providing statistical guarantees, including control over the Type I error rate, without heavily impacting the system's ability to detect anomalies. Building upon the principles of conformal prediction, the newly introduced framework of cross-conformal anomaly detection strikes a balance between statistical and computational efficiency. This framework is composed of five key methods: JackknifeAD, Jackknife+AD, CVAD, CV+AD, and Jackknife+-after-BootstrapAD.

Comparative Evaluation of Methods

The empirical evaluation illustrates that cross-conformal anomaly detection methods possess the ability to maintain reliable FDR control while achieving superior statistical power across various datasets. Unlike split-conformal methods, which previously defined the benchmark, cross-conformal methods exhibit lower variability and greater stability, making them particularly effective for handling small to medium-sized datasets. The evaluation process underscored the importance of methodical parameterization, especially concerning the cross-validation folds, to optimize the balance between model training and calibration.

Practical Applications and Implications

The introduction of cross-conformal methods to anomaly detection presents a significant advancement with practical implications across multiple sectors. These methods enhance model reliability by offering more precise anomaly detection. The versatility and model-agnostic nature of cross-conformal methods allow for their seamless integration into existing anomaly detection systems, further broadening their applicability. Moreover, the inherent features of these methods, such as improved estimator stability and the potential for higher detection sensitivity, position them as viable tools for critical applications where false detections carry significant consequences.

Future Directions in Cross-Conformal Anomaly Detection

While this work lays a foundational framework for cross-conformal anomaly detection and its advantages, several avenues for future research are evident. These include exploring adaptive parameterization strategies for cross-conformal methods to optimize performance across varying dataset sizes and characteristics. Additionally, extending cross-conformal methods to online anomaly detection settings represents a compelling area of inquiry, potentially broadening the applicability of these techniques. Further research could also investigate the integration of more complex anomaly detection algorithms within the cross-conformal framework, potentially enhancing detection capabilities and system robustness.

Conclusion

The shift towards cross-conformal anomaly detection methods embodies a significant evolution in the quest for reliable, explainable, and statistically robust anomaly detection systems. By providing comprehensive empirical evidence of their efficacy and discussing their practical implications, this paper contributes a valuable perspective to the ongoing development of advanced anomaly detection methodologies. As machine learning systems continue to permeate critical sectors, the continued refinement and application of cross-conformal anomaly detection methods will play a crucial role in ensuring these systems' trustworthiness and effectiveness.