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

TL;DR

This paper introduces a DNN-based MoM-GAN approach for robust distribution estimation of contaminated data, providing theoretical error bounds and demonstrating superior performance in real applications.

Contribution

It develops a novel MoM-GAN method combining GANs with median-of-mean estimation and derives non-asymptotic error bounds for contaminated data scenarios.

Findings

The error bound decreases as $n^{-b/p} \,\vee\, n^{-1/2}$ with sample size and dimension.

The MoM-GAN outperforms other methods on contaminated data in real tests.

The paper provides an implementable algorithm for the proposed method.

Abstract

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\"{o}lder class. The error bound decreases essentially as $n^{-b/p}\vee n^{-1/2}$, 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.