{
  "id": "1810.02030",
  "version": "v1",
  "published": "2018-10-04T02:37:16.000Z",
  "updated": "2018-10-04T02:37:16.000Z",
  "title": "Robust Estimation and Generative Adversarial Nets",
  "authors": [
    "Chao Gao",
    "Jiyi Liu",
    "Yuan Yao",
    "Weizhi Zhu"
  ],
  "categories": [
    "stat.ML",
    "cs.LG",
    "math.ST",
    "stat.CO",
    "stat.ME",
    "stat.TH"
  ],
  "abstract": "Robust estimation under Huber's $\\epsilon$-contamination model has become an important topic in statistics and theoretical computer science. Rate-optimal procedures such as Tukey's median and other estimators based on statistical depth functions are impractical because of their computational intractability. In this paper, we establish an intriguing connection between f-GANs and various depth functions through the lens of f-Learning. Similar to the derivation of f-GAN, we show that these depth functions that lead to rate-optimal robust estimators can all be viewed as variational lower bounds of the total variation distance in the framework of f-Learning. This connection opens the door of computing robust estimators using tools developed for training GANs. In particular, we show that a JS-GAN that uses a neural network discriminator with at least one hidden layer is able to achieve the minimax rate of robust mean estimation under Huber's $\\epsilon$-contamination model. Interestingly, the hidden layers for the neural net structure in the discriminator class is shown to be necessary for robust estimation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-04T02:37:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "robust estimation",
      "generative adversarial nets",
      "depth functions",
      "contamination model",
      "hidden layer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}