arXiv Machine Learning By Elaheh Akbari, James Liu, Keaton Hamm, Soheil Kolouri

Sliced Wasserstein Sketches with Error Certificates

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The paper introduces compact representations called sliced Wasserstein sketches that enable efficient, geometrically meaningful comparisons of probability distributions. It presents an exact decomposition of the squared distance error into residual and partition‑mismatch components, providing computable error certificates for any centroid sketch. Experiments demonstrate that optimal sketches reduce storage while maintaining classification performance, improve generalization with limited labels, and can be used as compact pooling layers in end‑to‑end learning.

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arXiv Machine Learning
Oct 12

Linearized Wasserstein dimensionality reduction with approximation guarantees

The paper introduces LOT Wassmap, an algorithm designed to uncover low‑dimensional structures in the Wasserstein space without computing a full pairwise distance matrix. It leverages approximation schemes such as Sinkhorn distances and linearized optimal transport to accelerate computations, and provides theoretical guarantees on embedding quality even when only finite samples are available. Experiments show that LOT Wassmap achieves accurate embeddings that improve with larger sample sizes while significantly reducing computational cost compared to traditional pairwise‑distance‑based methods.

By Alexander Cloninger, Keaton Hamm, Varun Khurana, Caroline Moosm\"uller