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

arXiv 2212.13741 ↗First posted 28 Dec 2022stat.ML cs.LG math.STcited by 0

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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.

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References · 17

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5 more
  1. 2019Deconstructing Generative Adversarial Networkscited by 15
  2. 2020Risk Bounds for Robust Deep Learningcited by 9
  3. 2021Robust W-GAN-Based Estimation Under Wasserstein Contaminationcited by 9
  4. 2022Non-Asymptotic Guarantees for Robust Statistical Learning under Infinite Variance Assumptioncited by 6
  5. 2021DeepMoM: Robust Deep Learning With Median-of-Meanscited by 2

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