{
  "id": "1506.07677",
  "version": "v1",
  "published": "2015-06-25T09:40:51.000Z",
  "updated": "2015-06-25T09:40:51.000Z",
  "title": "Manifold Optimization for Gaussian Mixture Models",
  "authors": [
    "Reshad Hosseini",
    "Suvrit Sra"
  ],
  "comment": "19 pages",
  "categories": [
    "stat.ML",
    "cs.LG",
    "math.OC"
  ],
  "abstract": "We take a new look at parameter estimation for Gaussian Mixture Models (GMMs). In particular, we propose using \\emph{Riemannian manifold optimization} as a powerful counterpart to Expectation Maximization (EM). An out-of-the-box invocation of manifold optimization, however, fails spectacularly: it converges to the same solution but vastly slower. Driven by intuition from manifold convexity, we then propose a reparamerization that has remarkable empirical consequences. It makes manifold optimization not only match EM---a highly encouraging result in itself given the poor record nonlinear programming methods have had against EM so far---but also outperform EM in many practical settings, while displaying much less variability in running times. We further highlight the strengths of manifold optimization by developing a somewhat tuned manifold LBFGS method that proves even more competitive and reliable than existing manifold optimization tools. We hope that our results encourage a wider consideration of manifold optimization for parameter estimation problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-25T09:40:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian mixture models",
      "em-a highly encouraging result",
      "parameter estimation",
      "poor record nonlinear programming methods",
      "somewhat tuned manifold lbfgs method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150607677H"
    }
  }
}