# Distribution Estimation of Contaminated Data via DNN-based MoM-GANs

arXiv: https://arxiv.org/abs/2212.13741 · HTML: https://mlsanity.com/paper/2212.13741/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 33 references that are in the map.
- First posted on arXiv 28 Dec 2022.

## Builds on (most cited first, 17 of 17)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [Generalization and Equilibrium in Generative Adversarial Nets (GANs)](https://mlsanity.com/paper/1703.00573/) (2017)
- [How Well Generative Adversarial Networks Learn Distributions](https://mlsanity.com/paper/1811.03179/) (2018)
- [An error analysis of generative adversarial networks for learning distributions](https://mlsanity.com/paper/2105.13010/) (2021)
- [Statistical Guarantees for Regularized Neural Networks](https://mlsanity.com/paper/2006.00294/) (2020)
- [Concentration Inequalities for Statistical Inference](https://mlsanity.com/paper/2011.02258/) (2020)
- [When OT meets MoM: Robust estimation of Wasserstein Distance](https://mlsanity.com/paper/2006.10325/) (2020)
- [On the capacity of deep generative networks for approximating distributions](https://mlsanity.com/paper/2101.12353/) (2021)
- [A Direct Approach to Robust Deep Learning Using Adversarial Networks](https://mlsanity.com/paper/1905.09591/) (2019)
- [Lecture Notes: Selected topics on robust statistical learning theory](https://mlsanity.com/paper/1908.10761/) (2019)
- [Deconstructing Generative Adversarial Networks](https://mlsanity.com/paper/1901.09465/) (2019)
- [Risk Bounds for Robust Deep Learning](https://mlsanity.com/paper/2009.06202/) (2020)
- [Robust W-GAN-Based Estimation Under Wasserstein Contamination](https://mlsanity.com/paper/2101.07969/) (2021)
- [Non-Asymptotic Guarantees for Robust Statistical Learning under Infinite Variance Assumption](https://mlsanity.com/paper/2201.03182/) (2022)
- [DeepMoM: Robust Deep Learning With Median-of-Means](https://mlsanity.com/paper/2105.14035/) (2021)

## Abstract (arXiv)

This paper studies the distribution estimation of contaminated data by the MoM-GAN method, which combines generative adversarial net (GAN) and median-of-mean (MoM) estimation. We use a deep neural network (DNN) with a ReLU activation function to model the generator and discriminator of the GAN. Theoretically, we derive a non-asymptotic error bound for the DNN-based MoM-GAN estimator measured by integral probability metrics with the b-smoothness H"older class. The error bound decreases essentially as n-b/pvee n-1/2, where n and p are the sample size and the dimension of input data. We give an algorithm for the MoM-GAN method and implement it through two real applications. The numerical results show that the MoM-GAN outperforms other competitive methods when dealing with contaminated data.