.png){kind=icon}
.png){kind=icon}
Return
ANOMALY DETECTION USING SHALLOW RELU NEURAL NETWORKS
.png){kind=icon}
PRE
AI
H
Z
DOI：10.3934/cpaa.2026052.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
Anomaly detection is an important task in many domains, and involves the identification of observations that deviate from normal data. Recent work has established theoretical results for deep ReLU neural networks under smoothness and noise assumptions, yet these results rely on extreme sparsity constraints that limit their practical use. In this work, we introduce shallow ReLU neural networks for unsupervised anomaly detection that retain the same theoretical guarantees. Under the Tsybakov noise condition and Ho & uml;lder smoothness of the underlying density, we prove that the empirical hinge risk minimiser consistently estimates the optimal Bayes classifier with an excess risk that vanishes as the sample size increases. These findings indicate that shallow ReLU neural network architectures can be a theoretically justified and computationally efficient alternative to deep neural network models for density level set based anomaly detection.
Keywords:
Anomaly detection
neural networks
regression
rates of convergence
noise condition
Journal
C
IF:
0.9
Papers:
88
Citations:
0
Organization
Cited Papers