Outlier Detection Using Generative Models with Theoretical Performance Guarantees

Jirong Yi; Jingchao Gao; Tianming Wang; Xiaodong Wu; Weiyu Xu

doi:10.1109/TIT.2024.3514636

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Outlier Detection Using Generative Models with Theoretical Performance Guarantees

Journal article

Peer reviewed

Outlier Detection Using Generative Models with Theoretical Performance Guarantees

Jirong Yi, Jingchao Gao, Tianming Wang, Xiaodong Wu and Weiyu Xu

IEEE transactions on information theory, Vol.71(5), pp.4012-4031

05/2025

DOI: 10.1109/TIT.2024.3514636

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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 by solving an ℓ 1 norm minimization problem. 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 and nonlinear generator neural networks with an arbitrary number of layers. We propose an iterative and linearized alternating direction method of multipliers (ADMM) algorithm for solving the outlier detection problem via ℓ 1 norm minimization, and a gradient descent algorithm for solving the outlier detection problem via squared ℓ 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 ℓ 2 norm minimization approach.

Magnetic Resonance Imaging

Analytical models

Anomaly detection

Deep learning

Extraterrestrial measurements

Generative model

Generators

Minimization

neural network

Neural networks

nonlinear activation function

outlier detection

Pollution measurement

recovery guarantees

Vectors

Details

Title: Subtitle: Outlier Detection Using Generative Models with Theoretical Performance Guarantees
Creators: Jirong Yi - University of Iowa, Electrical and Computer Engineering
Jingchao Gao - University of Iowa
Tianming Wang - University of Iowa
Xiaodong Wu - University of Iowa
Weiyu Xu - University of Iowa
Resource Type: Journal article
Publication Details: IEEE transactions on information theory, Vol.71(5), pp.4012-4031
DOI: 10.1109/TIT.2024.3514636
ISSN: 0018-9448
eISSN: 1557-9654
Publisher: IEEE
Grant note: 2000425; 2133205 / NSF
Language: English
Electronic publication date: 12/09/2024
Date published: 05/2025
Academic Unit: Electrical and Computer Engineering; Radiation Oncology; The Iowa Institute for Biomedical Imaging
Record Identifier: 9984757686902771

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