Robust Conformal Outlier Detection under Contaminated Reference Data
This addresses a practical issue in outlier detection for applications where perfectly labeled data is unavailable, offering a robust solution with theoretical guarantees, though it is incremental in enhancing existing conformal methods.
The paper tackles the problem of conformal outlier detection when reference data is contaminated with outliers, proving that calibration on such data yields conservative type-I error control but reduces power, and proposes an active data-cleaning framework that improves power without sacrificing validity, as validated by experiments on real datasets.
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.