{
  "id": "2006.12204",
  "version": "v1",
  "published": "2020-06-22T12:55:06.000Z",
  "updated": "2020-06-22T12:55:06.000Z",
  "title": "Telescoping Density-Ratio Estimation",
  "authors": [
    "Benjamin Rhodes",
    "Kai Xu",
    "Michael U. Gutmann"
  ],
  "categories": [
    "stat.ML",
    "cs.LG"
  ],
  "abstract": "Density-ratio estimation via classification is a cornerstone of unsupervised learning. It has provided the foundation for state-of-the-art methods in representation learning and generative modelling, with the number of use-cases continuing to proliferate. However, it suffers from a critical limitation: it fails to accurately estimate ratios p/q for which the two densities differ significantly. Empirically, we find this occurs whenever the KL divergence between p and q exceeds tens of nats. To resolve this limitation, we introduce a new framework, telescoping density-ratio estimation (TRE), that enables the estimation of ratios between highly dissimilar densities in high-dimensional spaces. Our experiments demonstrate that TRE can yield substantial improvements over existing single-ratio methods for mutual information estimation, representation learning and energy-based modelling.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-22T12:55:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "telescoping density-ratio estimation",
      "mutual information estimation",
      "yield substantial improvements",
      "accurately estimate ratios p/q",
      "state-of-the-art methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}