# Leave-One-Out-, Bootstrap- and Cross-Conformal Anomaly Detectors

arXiv: https://arxiv.org/abs/2402.16388 · HTML: https://mlsanity.com/paper/2402.16388/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 49 references that are in the map.
- First posted on arXiv 26 Feb 2024.

## Builds on (most cited first, 16 of 16)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [PyOD: A Python Toolbox for Scalable Outlier Detection](https://mlsanity.com/paper/1901.01588/) (2019)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [Deep Learning for Medical Anomaly Detection -- A Survey](https://mlsanity.com/paper/2012.02364/) (2020)
- [Learning by Transduction](https://mlsanity.com/paper/1301.7375/) (2013)
- [Predictive Inference Is Free with the Jackknife+-after-Bootstrap](https://mlsanity.com/paper/2002.09025/) (2020)
- [Real-time Out-of-distribution Detection in Learning-Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2001.10494/) (2020)
- [Prediction and outlier detection in classification problems](https://mlsanity.com/paper/1905.04396/) (2019)
- [Testing randomness](https://mlsanity.com/paper/1906.09256/) (2019)
- [Retrain or not retrain: Conformal test martingales for change-point detection](https://mlsanity.com/paper/2102.10439/) (2021)
- [A statistical framework for efficient out of distribution detection in deep neural networks](https://mlsanity.com/paper/2102.12967/) (2021)
- [Conformal k-NN Anomaly Detector for Univariate Data Streams](https://mlsanity.com/paper/1706.03412/) (2017)
- [Conformal Anomaly Detection on Spatio-Temporal Observations with Missing Data](https://mlsanity.com/paper/2105.11886/) (2021)
- [Anomaly Detection in Predictive Maintenance: A New Evaluation Framework for Temporal Unsupervised Anomaly Detection Algorithms](https://mlsanity.com/paper/2105.12818/) (2021)

## Built on by (most cited first, 4 of 4)

- [Between Resolution Collapse and Variance Inflation: Weighted Conformal Anomaly Detection in Low-Data Regimes](https://mlsanity.com/paper/2603.23205/) (2026)
- [Path Signatures Enable Model-Free Mapping of RNA Modifications](https://mlsanity.com/paper/2511.08855/) (2025)
- [Conformal Anomaly Detection in Python: Moving Beyond Heuristic Thresholds with nonconform](https://mlsanity.com/paper/2605.13642/) (2026)
- [How Many Categories Are Enough? Distribution-Free Certification Limits for Few-Shot Anomaly Thresholds](https://mlsanity.com/paper/2610.00236/) (2026)

## Abstract (arXiv)

The need for uncertainty quantification in anomaly detection systems has become increasingly important. In this context, effectively controlling Type I error rates without inflating Type II error rates in these systems can build trust and reduce costs associated with false discoveries. The field of conformal anomaly detection emerges as a promising approach for providing respective statistical and finite-sample validity guarantees through model calibration. However, reliance on calibration data imposes practical limitations, especially in low-data regimes. In this work, we formally define and evaluate leave-one-out-, bootstrap-, and cross-conformal methods for conformal anomaly detection, building on methods from the field of conformal prediction. Looking beyond the classical split-conformal approach, we show that derived methods for calculating resampling-conformal p-values offer a practical compromise between the data efficiency of full-conformal (transductive) approaches and the computational efficiency of split-conformal (inductive) methods. We validate derived methods and quantify their improvements for a range of one-class classifiers and datasets.