The Shape of Data: Intrinsic Distance for Data Distributions

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Dokumenter

  • Anton Tsitsulin, University of Bonn, Tyskland
  • Marina Munkhoeva, Skolkovo Inst Sci & Technol, Skolkovo Institute of Science & Technology, Massachusetts Institute of Technology (MIT), Rusland
  • Davide Mottin
  • Panagiotis Karras
  • Alex Bronstein, Technion-Israel Institute of Technology, Israel
  • Ivan Oseledets, Skolkovo Inst Sci & Technol, Skolkovo Institute of Science & Technology, Massachusetts Institute of Technology (MIT), Rusland
  • Emmanuel Müller, University of Bonn, Tyskland
Generative models are often used to sample high-dimensional data points from a manifold with small intrinsic dimension. Existing techniques for comparing generative models focus on global data properties such as mean and covariance; in that sense, they are extrinsic and uni-scale. We develop the first, to our knowledge, intrinsic and multi-scale method for characterizing and comparing underlying data manifolds, based on comparing all data moments by lower-bounding the spectral notion of the Gromov-Wasserstein distance between manifolds. In a thorough experimental study, we demonstrate that our method effectively evaluates the quality of generative models; further, we showcase its efficacy in discerning the disentanglement process in neural networks.
OriginalsprogEngelsk
TitelICLR 2020: Proceedings of the International Conference on Learning Representations
Udgivelsesår26 apr. 2020
StatusUdgivet - 26 apr. 2020

    Forskningsområder

  • stat.ML, cs.LG

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