{
  "id": "1710.02950",
  "version": "v1",
  "published": "2017-10-09T06:16:50.000Z",
  "updated": "2017-10-09T06:16:50.000Z",
  "title": "Maximum Regularized Likelihood Estimators: A General Prediction Theory and Applications",
  "authors": [
    "Rui Zhuang",
    "Johannes Lederer"
  ],
  "categories": [
    "stat.ML",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "Maximum regularized likelihood estimators (MRLEs) are arguably the most established class of estimators in high-dimensional statistics. In this paper, we derive guarantees for MRLEs in Kullback-Leibler divergence, a general measure of prediction accuracy. We assume only that the densities have a convex parametrization and that the regularization is definite and positive homogenous. The results thus apply to a very large variety of models and estimators, such as tensor regression and graphical models with convex and non-convex regularized methods. A main conclusion is that MRLEs are broadly consistent in prediction - regardless of whether restricted eigenvalues or similar conditions hold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-09T06:16:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximum regularized likelihood estimators",
      "general prediction theory",
      "applications",
      "similar conditions hold",
      "general measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}