论文标题
通过基于DNN的Mom-Gans对受污染数据的分布估计
Distribution Estimation of Contaminated Data via DNN-based MoM-GANs
论文作者
论文摘要
本文通过Mom-GAN方法研究了受污染数据的分布估计，该方法结合了生成对抗性网（GAN）和中位数（MOM）估计。我们使用具有Relu激活函数的深神经网络（DNN）来对GAN的发生器和歧视器进行建模。从理论上讲，我们得出了通过与$ b $ -smoothnessHölder类测量的基于DNN的MOM-GAN估计器绑定的非反应误差。错误限制的基本减少为$ n^{ - b/p} \ vee n^{ - 1/2} $，其中$ n $和$ p $是样本尺寸和输入数据的尺寸。我们为妈妈方法提供了一种算法，并通过两个实际应用程序实现它。数值结果表明，在处理受污染的数据时，妈妈的表现优于其他竞争方法。
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 Hölder 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.
