{
  "id": "1402.4844",
  "version": "v2",
  "published": "2014-02-19T22:57:03.000Z",
  "updated": "2016-05-26T14:06:50.000Z",
  "title": "Subspace Learning with Partial Information",
  "authors": [
    "Alon Gonen",
    "Dan Rosenbaum",
    "Yonina Eldar",
    "Shai Shalev-Shwartz"
  ],
  "categories": [
    "cs.LG",
    "stat.ML"
  ],
  "abstract": "The goal of subspace learning is to find a $k$-dimensional subspace of $\\mathbb{R}^d$, such that the expected squared distance between instance vectors and the subspace is as small as possible. In this paper we study subspace learning in a partial information setting, in which the learner can only observe $r \\le d$ attributes from each instance vector. We propose several efficient algorithms for this task, and analyze their sample complexity",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-19T22:57:03.000Z",
      "title": "The Sample Complexity of Subspace Learning with Partial Information",
      "abstract": "The goal of subspace learning is to find a $k$-dimensional subspace of $\\mathbb{R}^d$, such that the expected squared distance between instance vectors and the subspace is as small as possible. In this paper we study the sample complexity of subspace learning in a \\emph{partial information} setting, in which the learner can only observe $r \\le d$ attributes from each instance vector. We derive upper and lower bounds on the sample complexity in different scenarios. In particular, our upper bounds involve a generalization of vector sampling techniques, which are often used in bandit problems, to matrices.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-05-26T14:06:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sample complexity",
      "subspace learning",
      "partial information",
      "instance vector",
      "bandit problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.4844G"
    }
  }
}