This content will become publicly available on June 30, 2023

Unsupervised Anomaly Detection by Robust Density Estimation
Density estimation is a widely used method to perform unsupervised anomaly detection. By learning the density function, data points with relatively low densities are classified as anomalies. Unfortunately, the presence of anomalies in training data may significantly impact the density estimation process, thereby imposing significant challenges to the use of more sophisticated density estimation methods such as those based on deep neural networks. In this work, we propose RobustRealNVP, a deep density estimation framework that enhances the robustness of flow-based density estimation methods, enabling their application to unsupervised anomaly detection. RobustRealNVP differs from existing flow-based models from two perspectives. First, RobustRealNVP discards data points with low estimated densities during optimization to prevent them from corrupting the density estimation process. Furthermore, it imposes Lipschitz regularization to the flow-based model to enforce smoothness in the estimated density function. We demonstrate the robustness of our algorithm against anomalies in training data from both theoretical and empirical perspectives. The results show that our algorithm achieves competitive results as compared to state-of-the-art unsupervised anomaly detection methods.
Authors:
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Award ID(s):
Publication Date:
NSF-PAR ID:
10342093
Journal Name:
Proceedings of the AAAI Conference on Artificial Intelligence
Volume:
36
Issue:
4
Page Range or eLocation-ID:
4101 to 4108
ISSN:
2159-5399
2. Abstract Kernelized Gram matrix $W$ constructed from data points $\{x_i\}_{i=1}^N$ as $W_{ij}= k_0( \frac{ \| x_i - x_j \|^2} {\sigma ^2} )$ is widely used in graph-based geometric data analysis and unsupervised learning. An important question is how to choose the kernel bandwidth $\sigma$, and a common practice called self-tuned kernel adaptively sets a $\sigma _i$ at each point $x_i$ by the $k$-nearest neighbor (kNN) distance. When $x_i$s are sampled from a $d$-dimensional manifold embedded in a possibly high-dimensional space, unlike with fixed-bandwidth kernels, theoretical results of graph Laplacian convergence with self-tuned kernels have been incomplete. This paper proves the convergence of graph Laplacian operator $L_N$ to manifold (weighted-)Laplacian for a new family of kNN self-tuned kernels $W^{(\alpha )}_{ij} = k_0( \frac{ \| x_i - x_j \|^2}{ \epsilon \hat{\rho }(x_i) \hat{\rho }(x_j)})/\hat{\rho }(x_i)^\alpha \hat{\rho }(x_j)^\alpha$, where $\hat{\rho }$ is the estimated bandwidth function by kNN and the limiting operator is also parametrized by $\alpha$. When $\alpha = 1$, the limiting operator is the weighted manifold Laplacian $\varDelta _p$. Specifically, we prove the point-wise convergence of $L_N f$ and convergence of the graph Dirichlet form with rates. Our analysis is based on first establishing a $C^0$more »