Demeaned Sparse: Efficient Anomaly Detection by Residual Estimate

Yifan Fang, Yifei Fang, Ruizhe Chen, Haote Xu, Xinghao Ding, Yue Huang
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:15901-15924, 2025.

Abstract

Frequency-domain image anomaly detection methods can substantially enhance anomaly detection performance, however, they still lack an interpretable theoretical framework to guarantee the effectiveness of the detection process. We propose a novel test to detect anomalies in structural image via a Demeaned Fourier transform (DFT) under factor model framework, and we proof its effectiveness. We also briefly give the asymptotic theories of our test, the asymptotic theory explains why the test can detect anomalies at both the image and pixel levels within the theoretical lower bound. Based on our test, we derive a module called Demeaned Fourier Sparse (DFS) that effectively enhances detection performance in unsupervised anomaly detection tasks, which can construct masks in the Fourier domain and utilize a distribution-free sampling method similar to the bootstrap method. The experimental results indicate that this module can accurately and efficiently generate effective masks for reconstruction-based anomaly detection tasks, thereby enhancing the performance of anomaly detection methods and validating the effectiveness of the theoretical framework.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-fang25b, title = {Demeaned Sparse: Efficient Anomaly Detection by Residual Estimate}, author = {Fang, Yifan and Fang, Yifei and Chen, Ruizhe and Xu, Haote and Ding, Xinghao and Huang, Yue}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {15901--15924}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/fang25b/fang25b.pdf}, url = {https://proceedings.mlr.press/v267/fang25b.html}, abstract = {Frequency-domain image anomaly detection methods can substantially enhance anomaly detection performance, however, they still lack an interpretable theoretical framework to guarantee the effectiveness of the detection process. We propose a novel test to detect anomalies in structural image via a Demeaned Fourier transform (DFT) under factor model framework, and we proof its effectiveness. We also briefly give the asymptotic theories of our test, the asymptotic theory explains why the test can detect anomalies at both the image and pixel levels within the theoretical lower bound. Based on our test, we derive a module called Demeaned Fourier Sparse (DFS) that effectively enhances detection performance in unsupervised anomaly detection tasks, which can construct masks in the Fourier domain and utilize a distribution-free sampling method similar to the bootstrap method. The experimental results indicate that this module can accurately and efficiently generate effective masks for reconstruction-based anomaly detection tasks, thereby enhancing the performance of anomaly detection methods and validating the effectiveness of the theoretical framework.} }
Endnote
%0 Conference Paper %T Demeaned Sparse: Efficient Anomaly Detection by Residual Estimate %A Yifan Fang %A Yifei Fang %A Ruizhe Chen %A Haote Xu %A Xinghao Ding %A Yue Huang %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-fang25b %I PMLR %P 15901--15924 %U https://proceedings.mlr.press/v267/fang25b.html %V 267 %X Frequency-domain image anomaly detection methods can substantially enhance anomaly detection performance, however, they still lack an interpretable theoretical framework to guarantee the effectiveness of the detection process. We propose a novel test to detect anomalies in structural image via a Demeaned Fourier transform (DFT) under factor model framework, and we proof its effectiveness. We also briefly give the asymptotic theories of our test, the asymptotic theory explains why the test can detect anomalies at both the image and pixel levels within the theoretical lower bound. Based on our test, we derive a module called Demeaned Fourier Sparse (DFS) that effectively enhances detection performance in unsupervised anomaly detection tasks, which can construct masks in the Fourier domain and utilize a distribution-free sampling method similar to the bootstrap method. The experimental results indicate that this module can accurately and efficiently generate effective masks for reconstruction-based anomaly detection tasks, thereby enhancing the performance of anomaly detection methods and validating the effectiveness of the theoretical framework.
APA
Fang, Y., Fang, Y., Chen, R., Xu, H., Ding, X. & Huang, Y.. (2025). Demeaned Sparse: Efficient Anomaly Detection by Residual Estimate. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:15901-15924 Available from https://proceedings.mlr.press/v267/fang25b.html.

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