Robust Conformal Outlier Detection under Contaminated Reference Data

TL;DR

This paper investigates how conformal prediction methods behave with contaminated reference data in outlier detection, demonstrating their conservative nature and proposing an active data-cleaning approach to improve detection power while maintaining statistical guarantees.

Contribution

It provides a theoretical analysis of conformal methods under contaminated data and introduces a novel active cleaning framework to enhance outlier detection performance.

Findings

Conformal methods remain conservative under contamination, ensuring valid error control.

Active data cleaning improves detection power without losing validity.

Experimental results confirm the effectiveness of the proposed approach.

Abstract

Conformal prediction is a flexible framework for calibrating machine learning predictions, providing distribution-free statistical guarantees. In outlier detection, this calibration relies on a reference set of labeled inlier data to control the type-I error rate. However, obtaining a perfectly labeled inlier reference set is often unrealistic, and a more practical scenario involves access to a contaminated reference set containing a small fraction of outliers. This paper analyzes the impact of such contamination on the validity of conformal methods. We prove that under realistic, non-adversarial settings, calibration on contaminated data yields conservative type-I error control, shedding light on the inherent robustness of conformal methods. This conservativeness, however, typically results in a loss of power. To alleviate this limitation, we propose a novel, active data-cleaning framework that leverages a limited labeling budget and an outlier detection model to selectively annotate data points in the contaminated reference set that are suspected as outliers. By removing only the annotated outliers in this ``suspicious'' subset, we can effectively enhance power while mitigating the risk of inflating the type-I error rate, as supported by our theoretical analysis. Experiments on real datasets validate the conservative behavior of conformal methods under contamination and show that the proposed data-cleaning strategy improves power without sacrificing validity.