{
  "id": "2011.10797",
  "version": "v1",
  "published": "2020-11-21T14:14:12.000Z",
  "updated": "2020-11-21T14:14:12.000Z",
  "title": "Adversarial Classification: Necessary conditions and geometric flows",
  "authors": [
    "Nicolas Garcia Trillos",
    "Ryan Murray"
  ],
  "categories": [
    "cs.LG",
    "cs.CR",
    "math.AP",
    "stat.ML"
  ],
  "abstract": "We study a version of adversarial classification where an adversary is empowered to corrupt data inputs up to some distance $\\varepsilon$, using tools from variational analysis. In particular, we describe necessary conditions associated with the optimal classifier subject to such an adversary. Using the necessary conditions, we derive a geometric evolution equation which can be used to track the change in classification boundaries as $\\varepsilon$ varies. This evolution equation may be described as an uncoupled system of differential equations in one dimension, or as a mean curvature type equation in higher dimension. In one dimension we rigorously prove that one can use the initial value problem starting from $\\varepsilon=0$, which is simply the Bayes classifier, in order to solve for the global minimizer of the adversarial problem. Numerical examples illustrating these ideas are also presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-21T14:14:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "necessary conditions",
      "adversarial classification",
      "geometric flows",
      "mean curvature type equation",
      "geometric evolution equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}