{
  "id": "2401.16594",
  "version": "v2",
  "published": "2024-01-29T21:51:27.000Z",
  "updated": "2024-06-20T22:47:03.000Z",
  "title": "Consistent algorithms for multi-label classification with macro-at-$k$ metrics",
  "authors": [
    "Erik Schultheis",
    "Wojciech Kotłowski",
    "Marek Wydmuch",
    "Rohit Babbar",
    "Strom Borman",
    "Krzysztof Dembczyński"
  ],
  "comment": "This is the authors' version of the work accepted to ICLR 2024; the final version of the paper, errors and typos corrected, and minor modifications to improve clarity",
  "categories": [
    "cs.LG"
  ],
  "abstract": "We consider the optimization of complex performance metrics in multi-label classification under the population utility framework. We mainly focus on metrics linearly decomposable into a sum of binary classification utilities applied separately to each label with an additional requirement of exactly $k$ labels predicted for each instance. These \"macro-at-$k$\" metrics possess desired properties for extreme classification problems with long tail labels. Unfortunately, the at-$k$ constraint couples the otherwise independent binary classification tasks, leading to a much more challenging optimization problem than standard macro-averages. We provide a statistical framework to study this problem, prove the existence and the form of the optimal classifier, and propose a statistically consistent and practical learning algorithm based on the Frank-Wolfe method. Interestingly, our main results concern even more general metrics being non-linear functions of label-wise confusion matrices. Empirical results provide evidence for the competitive performance of the proposed approach.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-06-20T22:47:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multi-label classification",
      "consistent algorithms",
      "independent binary classification tasks",
      "population utility framework",
      "long tail labels"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}