  Given the growing significance of reliable, trustworthy, and explainable
machine learning, 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, particularly when follow-up procedures are
expensive. Leveraging the principles of conformal prediction emerges as a
promising approach for providing respective statistical guarantees by
calibrating a model's uncertainty. This work introduces a novel framework for
anomaly detection, termed cross-conformal anomaly detection, building upon
well-known cross-conformal methods designed for prediction tasks. With that, it
addresses a natural research gap by extending previous works in the context of
inductive conformal anomaly detection, relying on the split-conformal approach
for model calibration. Drawing on insights from conformal prediction, we
demonstrate that the derived methods for calculating cross-conformal $p$-values
strike a practical compromise between statistical efficiency (full-conformal)
and computational efficiency (split-conformal) for uncertainty-quantified
anomaly detection on benchmark datasets.
