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.

本研究解决了无监督异常检测缺乏理论保障的问题，提出通过将其转化为二分类问题，建立了神经网络的额外风险的非渐近上界和收敛速率。研究发现，优化模型能够达到文献中最优的极小最大速率，同时提供了实现最佳性能所需的合成异常数量的界限。

基于分类的神经网络最佳异常检测：理论与实践