Statistical guarantees for distribution estimation of contaminated data via DNN-based MoM-GANs

Abstract

This paper investigates the distribution estimation of contaminated data using the MoM-GAN method, which leverages the power of generative adversarial nets (GANs) and median-of-means (MoM) estimation. Specifically, we use a deep neural network (DNN) with a ReLU activation function to model the generator and discriminator of the GAN. In terms of theoretical analysis, we derive a non-asymptotic error bound for the DNN-based MoM-GAN estimator, which is measured by integral probability metrics and takes into account the $b$-smoothness Hölder class. The error bound essentially decreases in $n^{-b/p}\vee n^{-1/2}$, where $n$ and $p$ are the sample size and the dimension of the input data, respectively. It provides a rigorous guarantee of the accuracy and robustness of the MoM-GAN estimator, even in the presence of contaminated data. We present an algorithm for the MoM-GAN method and demonstrate its effectiveness in two real-world applications. Our results show that the MoM-GAN method outperforms other competing methods when dealing with contaminated data, highlighting its superior performance and robustness.