Sliced Wasserstein Sketches with Error Certificates
Compact representations that support geometrically meaningful comparisons are valuable for learning from probability distributions. 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. Using $L$ shared projections yields a sketch with $O(LM)$ comparison time. Our main result is an exact decomposition of squared distance error into residual and partition-mismatch terms, yielding computable certificates for arbitrary centroid sketches. For optimal sketches, a finite $(2+δ)$ moment for some $δ>0$ guarantees $O(M^{-1})$ error in the finite-direction sliced distance, while e...
| Authors | Elaheh Akbari, James Liu, Keaton Hamm et al. |
|---|---|
| Primary category | cs.LG |
| Published | 14 October 2026 |
| Last updated at source | 14 October 2026 |
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