{
  "id": "2006.10293",
  "version": "v1",
  "published": "2020-06-18T06:11:28.000Z",
  "updated": "2020-06-18T06:11:28.000Z",
  "title": "GAT-GMM: Generative Adversarial Training for Gaussian Mixture Models",
  "authors": [
    "Farzan Farnia",
    "William Wang",
    "Subhro Das",
    "Ali Jadbabaie"
  ],
  "categories": [
    "cs.LG",
    "stat.ML"
  ],
  "abstract": "Generative adversarial networks (GANs) learn the distribution of observed samples through a zero-sum game between two machine players, a generator and a discriminator. While GANs achieve great success in learning the complex distribution of image, sound, and text data, they perform suboptimally in learning multi-modal distribution-learning benchmarks including Gaussian mixture models (GMMs). In this paper, we propose Generative Adversarial Training for Gaussian Mixture Models (GAT-GMM), a minimax GAN framework for learning GMMs. Motivated by optimal transport theory, we design the zero-sum game in GAT-GMM using a random linear generator and a softmax-based quadratic discriminator architecture, which leads to a non-convex concave minimax optimization problem. We show that a Gradient Descent Ascent (GDA) method converges to an approximate stationary minimax point of the GAT-GMM optimization problem. In the benchmark case of a mixture of two symmetric, well-separated Gaussians, we further show this stationary point recovers the true parameters of the underlying GMM. We numerically support our theoretical findings by performing several experiments, which demonstrate that GAT-GMM can perform as well as the expectation-maximization algorithm in learning mixtures of two Gaussians.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-18T06:11:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian mixture models",
      "generative adversarial training",
      "non-convex concave minimax optimization problem",
      "zero-sum game",
      "gans achieve great success"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}