Lipschitz Continuous Autoencoders in Application to Anomaly Detection

Young-geun Kim, Yongchan Kwon, Hyunwoong Chang, Myunghee Cho Paik
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:2507-2517, 2020.

Abstract

Anomaly detection is the task of finding abnormal data that are distinct from normal behavior. Current deep learning-based anomaly detection methods train neural networks with normal data alone and calculate anomaly scores based on the trained model. In this work, we formalize current practices, build a theoretical framework of anomaly detection algorithms equipped with an objective function and a hypothesis space, and establish a desirable property of the anomaly detection algorithm, namely, admissibility. Admissibility implies that optimal autoencoders for normal data yield a larger reconstruction error for anomalous data than that for normal data on average. We then propose a class of admissible anomaly detection algorithms equipped with an integral probability metric-based objective function and a class of autoencoders, Lipschitz continuous autoencoders. The proposed algorithm for Wasserstein distance is implemented by minimizing an approximated Wasserstein distance with a penalty to enforce Lipschitz continuity with respect to Wasserstein distance. Through ablation studies, we demonstrate the efficacy of enforcing Lipschitz continuity of the proposed method. The proposed method is shown to be more effective in detecting anomalies than existing methods via applications to network traffic and image datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v108-kim20c, title = {Lipschitz Continuous Autoencoders in Application to Anomaly Detection}, author = {Kim, Young-geun and Kwon, Yongchan and Chang, Hyunwoong and Paik, Myunghee Cho}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {2507--2517}, year = {2020}, editor = {Chiappa, Silvia and Calandra, Roberto}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/kim20c/kim20c.pdf}, url = {https://proceedings.mlr.press/v108/kim20c.html}, abstract = {Anomaly detection is the task of finding abnormal data that are distinct from normal behavior. Current deep learning-based anomaly detection methods train neural networks with normal data alone and calculate anomaly scores based on the trained model. In this work, we formalize current practices, build a theoretical framework of anomaly detection algorithms equipped with an objective function and a hypothesis space, and establish a desirable property of the anomaly detection algorithm, namely, admissibility. Admissibility implies that optimal autoencoders for normal data yield a larger reconstruction error for anomalous data than that for normal data on average. We then propose a class of admissible anomaly detection algorithms equipped with an integral probability metric-based objective function and a class of autoencoders, Lipschitz continuous autoencoders. The proposed algorithm for Wasserstein distance is implemented by minimizing an approximated Wasserstein distance with a penalty to enforce Lipschitz continuity with respect to Wasserstein distance. Through ablation studies, we demonstrate the efficacy of enforcing Lipschitz continuity of the proposed method. The proposed method is shown to be more effective in detecting anomalies than existing methods via applications to network traffic and image datasets.} }
Endnote
%0 Conference Paper %T Lipschitz Continuous Autoencoders in Application to Anomaly Detection %A Young-geun Kim %A Yongchan Kwon %A Hyunwoong Chang %A Myunghee Cho Paik %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-kim20c %I PMLR %P 2507--2517 %U https://proceedings.mlr.press/v108/kim20c.html %V 108 %X Anomaly detection is the task of finding abnormal data that are distinct from normal behavior. Current deep learning-based anomaly detection methods train neural networks with normal data alone and calculate anomaly scores based on the trained model. In this work, we formalize current practices, build a theoretical framework of anomaly detection algorithms equipped with an objective function and a hypothesis space, and establish a desirable property of the anomaly detection algorithm, namely, admissibility. Admissibility implies that optimal autoencoders for normal data yield a larger reconstruction error for anomalous data than that for normal data on average. We then propose a class of admissible anomaly detection algorithms equipped with an integral probability metric-based objective function and a class of autoencoders, Lipschitz continuous autoencoders. The proposed algorithm for Wasserstein distance is implemented by minimizing an approximated Wasserstein distance with a penalty to enforce Lipschitz continuity with respect to Wasserstein distance. Through ablation studies, we demonstrate the efficacy of enforcing Lipschitz continuity of the proposed method. The proposed method is shown to be more effective in detecting anomalies than existing methods via applications to network traffic and image datasets.
APA
Kim, Y., Kwon, Y., Chang, H. & Paik, M.C.. (2020). Lipschitz Continuous Autoencoders in Application to Anomaly Detection. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:2507-2517 Available from https://proceedings.mlr.press/v108/kim20c.html.

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