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The Shape of Data: Intrinsic Distance for Data Distributions

Samples from two distributions
Two distributions having the same first 3 moments, meaning popular GAN scores are close to 0.

paper · pdf · arXiv · code

TL;DR

IMD is a new metric for comparing data distributions based on their geometry:

  • Fast — $O(n)$ in the number of data samples
  • Extrinsic — does not rely on any positional information
  • Multiscale — approximates and compares all moments of distributions