Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.08521 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912025886588928 |
|---|---|
| author | Zhou, Tian-Yi Lau, Matthew Chen, Jizhou Lee, Wenke Huo, Xiaoming |
| author_facet | Zhou, Tian-Yi Lau, Matthew Chen, Jizhou Lee, Wenke Huo, Xiaoming |
| contents | Anomaly detection is an important problem in many application areas, such as network security. Many deep learning methods for unsupervised anomaly detection produce good empirical performance but lack theoretical guarantees. By casting anomaly detection into a binary classification problem, we establish non-asymptotic upper bounds and a convergence rate on the excess risk on rectified linear unit (ReLU) neural networks trained on synthetic anomalies. Our convergence rate on the excess risk matches the minimax optimal rate in the literature. Furthermore, we provide lower and upper bounds on the number of synthetic anomalies that can attain this optimality. For practical implementation, we relax some conditions to improve the search for the empirical risk minimizer, which leads to competitive performance to other classification-based methods for anomaly detection. Overall, our work provides the first theoretical guarantees of unsupervised neural network-based anomaly detectors and empirical insights on how to design them well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08521 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal Classification-based Anomaly Detection with Neural Networks: Theory and Practice Zhou, Tian-Yi Lau, Matthew Chen, Jizhou Lee, Wenke Huo, Xiaoming Machine Learning Cryptography and Security Statistics Theory Anomaly detection is an important problem in many application areas, such as network security. Many deep learning methods for unsupervised anomaly detection produce good empirical performance but lack theoretical guarantees. By casting anomaly detection into a binary classification problem, we establish non-asymptotic upper bounds and a convergence rate on the excess risk on rectified linear unit (ReLU) neural networks trained on synthetic anomalies. Our convergence rate on the excess risk matches the minimax optimal rate in the literature. Furthermore, we provide lower and upper bounds on the number of synthetic anomalies that can attain this optimality. For practical implementation, we relax some conditions to improve the search for the empirical risk minimizer, which leads to competitive performance to other classification-based methods for anomaly detection. Overall, our work provides the first theoretical guarantees of unsupervised neural network-based anomaly detectors and empirical insights on how to design them well. |
| title | Optimal Classification-based Anomaly Detection with Neural Networks: Theory and Practice |
| topic | Machine Learning Cryptography and Security Statistics Theory |
| url | https://arxiv.org/abs/2409.08521 |