{
  "id": "2211.15322",
  "version": "v1",
  "published": "2022-11-28T14:00:50.000Z",
  "updated": "2022-11-28T14:00:50.000Z",
  "title": "Transductive Kernels for Gaussian Processes on Graphs",
  "authors": [
    "Yin-Cong Zhi",
    "Felix L. Opolka",
    "Yin Cheng Ng",
    "Pietro Liò",
    "Xiaowen Dong"
  ],
  "categories": [
    "cs.LG",
    "stat.ML"
  ],
  "abstract": "Kernels on graphs have had limited options for node-level problems. To address this, we present a novel, generalized kernel for graphs with node feature data for semi-supervised learning. The kernel is derived from a regularization framework by treating the graph and feature data as two Hilbert spaces. We also show how numerous kernel-based models on graphs are instances of our design. A kernel defined this way has transductive properties, and this leads to improved ability to learn on fewer training points, as well as better handling of highly non-Euclidean data. We demonstrate these advantages using synthetic data where the distribution of the whole graph can inform the pattern of the labels. Finally, by utilizing a flexible polynomial of the graph Laplacian within the kernel, the model also performed effectively in semi-supervised classification on graphs of various levels of homophily.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-28T14:00:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian processes",
      "transductive kernels",
      "node feature data",
      "node-level problems",
      "hilbert spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}