{
  "id": "1506.07613",
  "version": "v1",
  "published": "2015-06-25T04:56:50.000Z",
  "updated": "2015-06-25T04:56:50.000Z",
  "title": "Generalized Majorization-Minimization",
  "authors": [
    "Sobhan Naderi Parizi",
    "Kun He",
    "Stan Sclaroff",
    "Pedro Felzenszwalb"
  ],
  "categories": [
    "cs.CV",
    "cs.IT",
    "cs.LG",
    "math.IT",
    "stat.ML"
  ],
  "abstract": "Non-convex optimization is ubiquitous in machine learning. The Majorization-Minimization (MM) procedure systematically optimizes non-convex functions through an iterative construction and optimization of upper bounds on the objective function. The bound at each iteration is required to \\emph{touch} the objective function at the optimizer of the previous bound. We show that this touching constraint is unnecessary and overly restrictive. We generalize MM by relaxing this constraint, and propose a new framework for designing optimization algorithms, named Generalized Majorization-Minimization (G-MM). Compared to MM, G-MM is much more flexible. For instance, it can incorporate application-specific biases into the optimization procedure without changing the objective function. We derive G-MM algorithms for several latent variable models and show that they consistently outperform their MM counterparts in optimizing non-convex objectives. In particular, G-MM algorithms appear to be less sensitive to initialization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-25T04:56:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalized majorization-minimization",
      "objective function",
      "procedure systematically optimizes non-convex functions",
      "incorporate application-specific biases",
      "g-mm algorithms appear"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}