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Outlier Detection Using Generative Models with Theoretical Performance Guarantees
Preprint   Open access

Outlier Detection Using Generative Models with Theoretical Performance Guarantees

Jirong Yi, Jingchao Gao, Tianming Wang, Xiaodong Wu and Weiyu Xu
arXiv.org
Cornell University Library, arXiv.org
10/16/2023
DOI: 10.48550/arxiv.2310.09999
url
https://doi.org/10.48550/arxiv.2310.09999View
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

This paper considers the problem of recovering signals modeled by generative models from linear measurements contaminated with sparse outliers. We propose an outlier detection approach for reconstructing the ground-truth signals modeled by generative models under sparse outliers. We establish theoretical recovery guarantees for reconstruction of signals using generative models in the presence of outliers, giving lower bounds on the number of correctable outliers. Our results are applicable to both linear generator neural networks and the nonlinear generator neural networks with an arbitrary number of layers. We propose an iterative alternating direction method of multipliers (ADMM) algorithm for solving the outlier detection problem via \(\ell_1\) norm minimization, and a gradient descent algorithm for solving the outlier detection problem via squared \(\ell_1\) norm minimization. We conduct extensive experiments using variational auto-encoder and deep convolutional generative adversarial networks, and the experimental results show that the signals can be successfully reconstructed under outliers using our approach. Our approach outperforms the traditional Lasso and \(\ell_2\) minimization approach.
 Algorithms Data Analysis Optimization Generative adversarial networks Iterative methods Lower bounds Neural networks Outliers (statistics)

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