{
  "id": "1207.4255",
  "version": "v2",
  "published": "2012-07-18T02:53:02.000Z",
  "updated": "2015-10-24T08:11:13.000Z",
  "title": "On the Statistical Efficiency of $\\ell_{1,p}$ Multi-Task Learning of Gaussian Graphical Models",
  "authors": [
    "Jean Honorio",
    "Tommi Jaakkola",
    "Dimitris Samaras"
  ],
  "comment": "Submitted on October 21, 2015 to the Journal of Machine Learning Research",
  "categories": [
    "cs.LG",
    "stat.ML"
  ],
  "abstract": "In this paper, we present $\\ell_{1,p}$ multi-task structure learning for Gaussian graphical models. We analyze the sufficient number of samples for the correct recovery of the support union and edge signs. We also analyze the necessary number of samples for any conceivable method by providing information-theoretic lower bounds. We compare the statistical efficiency of multi-task learning versus that of single-task learning. For experiments, we use a block coordinate descent method that is provably convergent and generates a sequence of positive definite solutions. We provide experimental validation on synthetic data as well as on two publicly available real-world data sets, including functional magnetic resonance imaging and gene expression data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-18T02:53:02.000Z",
      "title": "Simultaneous and Group-Sparse Multi-Task Learning of Gaussian Graphical Models",
      "abstract": "In this paper, we present $\\ell_{1,p}$ multi-task structure learning for Gaussian graphical models. We discuss the uniqueness and boundedness of the optimal solution of the maximization problem. A block coordinate descent method leads to a provably convergent algorithm that generates a sequence of positive definite solutions. Thus, we reduce the original problem into a sequence of strictly convex $\\ell_p$ regularized quadratic minimization subproblems. We further show that this subproblem leads to the continuous quadratic knapsack problem for $p=\\infty$ and to a separable version of the well-known quadratic trust-region problem for $p=2$, for which very efficient methods exist. Finally, we show promising results in synthetic experiments as well as in two real-world datasets.",
      "comment": "Submitted on April 23, 2012 to JMLR",
      "journal": null,
      "doi": null,
      "authors": [
        "Jean Honorio",
        "Dimitris Samaras"
      ]
    },
    {
      "version": "v2",
      "updated": "2015-10-24T08:11:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian graphical models",
      "group-sparse multi-task learning",
      "well-known quadratic trust-region problem",
      "block coordinate descent method",
      "continuous quadratic knapsack problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.4255H"
    }
  }
}