# Tight Rates in Supervised Outlier Transfer Learning

arXiv: https://arxiv.org/abs/2310.04686 · HTML: https://mlsanity.com/paper/2310.04686/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 36 references that are in the map.
- First posted on arXiv 7 Oct 2023.

## Builds on (most cited first, 10 of 10)

- [Anomaly Detection using One-Class Neural Networks](https://mlsanity.com/paper/1802.06360/) (2018)
- [On the Value of Target Data in Transfer Learning](https://mlsanity.com/paper/2002.04747/) (2020)
- [Near-Optimal Linear Regression under Distribution Shift](https://mlsanity.com/paper/2106.12108/) (2021)
- [Time Series Anomaly Detection Using Convolutional Neural Networks and Transfer Learning](https://mlsanity.com/paper/1905.13628/) (2019)
- [Minimax Lower Bounds for Transfer Learning with Linear and One-hidden Layer Neural Networks](https://mlsanity.com/paper/2006.10581/) (2020)
- [A No-Free-Lunch Theorem for MultiTask Learning](https://mlsanity.com/paper/2006.15785/) (2020)
- [A Generalized Neyman-Pearson Criterion for Optimal Domain Adaptation](https://mlsanity.com/paper/1810.01545/) (2018)
- [Anomaly Detection with Domain Adaptation](https://mlsanity.com/paper/2006.03689/) (2020)
- [EDIMA: Early Detection of IoT Malware Network Activity Using Machine Learning Techniques](https://mlsanity.com/paper/1906.09715/) (2019)
- [A Transfer Learning Framework for Anomaly Detection Using Model of Normality](https://mlsanity.com/paper/2011.06210/) (2020)

## Built on by (most cited first, 3 of 3)

- [Neyman-Pearson Classification under Both Null and Alternative Distributions Shift](https://mlsanity.com/paper/2511.06641/) (2025)
- [An Efficient Variant of One-Class SVM with Lifelong Online Learning Guarantees](https://mlsanity.com/paper/2512.11052/) (2025)
- [Classification with Abstention Under Class-Conditional Error Constraints](https://mlsanity.com/paper/2609.22632/) (2026)

## Abstract (arXiv)

A critical barrier to learning an accurate decision rule for outlier detection is the scarcity of outlier data. As such, practitioners often turn to the use of similar but imperfect outlier data from which they might transfer information to the target outlier detection task. Despite the recent empirical success of transfer learning approaches in outlier detection, a fundamental understanding of when and how knowledge can be transferred from a source to a target outlier detection task remains elusive. In this work, we adopt the traditional framework of Neyman-Pearson classification -- which formalizes supervised outlier detection -- with the added assumption that one has access to some related but imperfect outlier data. Our main results are as follows: We first determine the information-theoretic limits of the problem under a measure of discrepancy that extends some existing notions from traditional balanced classification; interestingly, unlike in balanced classification, seemingly very dissimilar sources can provide much information about a target, thus resulting in fast transfer. We then show that, in principle, these information-theoretic limits are achievable by adaptive procedures, i.e., procedures with no a priori information on the discrepancy between source and target outlier distributions.