Sliced Wasserstein Sketches with Error Certificates

Key points

• Compact representations that support geometrically meaningful comparisons are valuable for learning from probability distributions.1
• Our main result is an exact decomposition of squared distance error into residual and partition-mismatch terms, yielding computable certificates for arbitrary centroid sketches.1
• For optimal sketches, a finite $(2+δ)$ moment for some $δ>0$ guarantees $O(M^{-1})$ error in the finite-direction sliced distance, while equal-mass sketches can converge more slowly.1
• Experiments on document, point-cloud, and flow-cytometry benchmarks show that optimal sketches substantially reduce storage while preserving the classification performance of uncompressed sliced distances.1

Sources (1)

• [1]Sliced Wasserstein Sketches with Error Certificates
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 14, 06:32 PM

  We study optimal, free-weight $M$-atom quantization of one-dimensional probability measures in quadratic Wasserstein distance and extend it to higher dimensions via slicing.

  Compact representations that support geometrically meaningful comparisons are valuable for learning from probability distributions.

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