# Outlier Detection Using Generative Models with Theoretical Performance Guarantees

arXiv: https://arxiv.org/abs/2310.09999 · HTML: https://mlsanity.com/paper/2310.09999/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 63 references that are in the map.
- First posted on arXiv 16 Oct 2023.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Towards Real-World Blind Face Restoration with Generative Facial Prior](https://mlsanity.com/paper/2101.04061/) (2021)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [DiffBIR: Towards Blind Image Restoration with Generative Diffusion Prior](https://mlsanity.com/paper/2308.15070/) (2023)
- [StyleGAN-T: Unlocking the Power of GANs for Fast Large-Scale Text-to-Image Synthesis](https://mlsanity.com/paper/2301.09515/) (2023)
- [Generative Diffusion Prior for Unified Image Restoration and Enhancement](https://mlsanity.com/paper/2304.01247/) (2023)
- [StarGAN-VC: Non-parallel many-to-many voice conversion with star generative adversarial networks](https://mlsanity.com/paper/1806.02169/) (2018)
- [CNN-Based Projected Gradient Descent for Consistent Image Reconstruction](https://mlsanity.com/paper/1709.01809/) (2017)
- [Learned D-AMP: Principled Neural Network based Compressive Image Recovery](https://mlsanity.com/paper/1704.06625/) (2017)
- [Robust Regression via Hard Thresholding](https://mlsanity.com/paper/1506.02428/) (2015)
- [Modeling Sparse Deviations for Compressed Sensing using Generative Models](https://mlsanity.com/paper/1807.01442/) (2018)
- [ADMM-Net: A Deep Learning Approach for Compressive Sensing MRI](https://mlsanity.com/paper/1705.06869/) (2017)
- [Stable Deep MRI Reconstruction using Generative Priors](https://mlsanity.com/paper/2210.13834/) (2022)
- [Complexity of Proximal augmented Lagrangian for nonconvex optimization with nonlinear equality constraints](https://mlsanity.com/paper/1908.00131/) (2019)
- [Learning a Compressed Sensing Measurement Matrix via Gradient Unrolling](https://mlsanity.com/paper/1806.10175/) (2018)
- [Corrupted Sensing: Novel Guarantees for Separating Structured Signals](https://mlsanity.com/paper/1305.2524/) (2013)
- [Robust recovery of complex exponential signals from random Gaussian projections via low rank Hankel matrix reconstruction](https://mlsanity.com/paper/1503.02893/) (2015)
- [Detecting Outliers in Data with Correlated Measures](https://mlsanity.com/paper/1808.08640/) (2018)
- [Separation-Free Super-Resolution from Compressed Measurements is Possible: an Orthonormal Atomic Norm Minimization Approach](https://mlsanity.com/paper/1711.01396/) (2017)
- [Complexity of a linearized augmented Lagrangian method for nonconvex minimization with nonlinear equality constraints](https://mlsanity.com/paper/2301.08345/) (2023)

## Abstract (arXiv)

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 ℓ1 norm minimization, and a gradient descent algorithm for solving the outlier detection problem via squared ℓ1 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 ℓ2 minimization approach.