{
  "id": "1911.01483",
  "version": "v1",
  "published": "2019-11-04T20:48:30.000Z",
  "updated": "2019-11-04T20:48:30.000Z",
  "title": "Statistical Inference for Model Parameters in Stochastic Gradient Descent via Batch Means",
  "authors": [
    "Yi Zhu",
    "Jing Dong"
  ],
  "categories": [
    "stat.ML",
    "cs.LG",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "Statistical inference of true model parameters based on stochastic gradient descent (SGD) has started receiving attention in recent years. In this paper, we study a simple algorithm to construct asymptotically valid confidence regions for model parameters using the batch means method. The main idea is to cancel out the covariance matrix which is hard/costly to estimate. In the process of developing the algorithm, we establish process-level function central limit theorem for Polyak-Ruppert averaging based SGD estimators. We also extend the batch means method to accommodate more general batch size specifications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-04T20:48:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic gradient descent",
      "model parameters",
      "statistical inference",
      "asymptotically valid confidence regions",
      "batch means method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}