{
  "id": "2107.07115",
  "version": "v1",
  "published": "2021-07-15T04:40:02.000Z",
  "updated": "2021-07-15T04:40:02.000Z",
  "title": "Principal component analysis for Gaussian process posteriors",
  "authors": [
    "Hideaki Ishibashi",
    "Shotaro Akaho"
  ],
  "categories": [
    "stat.ML",
    "cs.LG"
  ],
  "abstract": "This paper proposes an extension of principal component analysis for Gaussian process posteriors denoted by GP-PCA. Since GP-PCA estimates a low-dimensional space of GP posteriors, it can be used for meta-learning, which is a framework for improving the precision of a new task by estimating a structure of a set of tasks. The issue is how to define a structure of a set of GPs with an infinite-dimensional parameter, such as coordinate system and a divergence. In this study, we reduce the infiniteness of GP to the finite-dimensional case under the information geometrical framework by considering a space of GP posteriors that has the same prior. In addition, we propose an approximation method of GP-PCA based on variational inference and demonstrate the effectiveness of GP-PCA as meta-learning through experiments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-15T04:40:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "principal component analysis",
      "gaussian process posteriors",
      "gp posteriors",
      "gp-pca estimates",
      "low-dimensional space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}