Reproduce “Distribution Regression with Sliced Wasserstein Kernels” on OpenResearch

About this paper

Dimitri Meunier, Massimiliano Pontil, Carlo Ciliberto

The authors introduce sliced Wasserstein kernels for distribution regression from finite sample bags, using projections, sorted quantiles, and Gaussian-like kernels in kernel ridge regression. The method works directly with empirical distributions, including discrete ones. On perturbed MNIST, SW₂ KRR reaches 0.82 accuracy versus 0.34 for MMD KRR, while unperturbed Fashion-MNIST slightly favors an RBF baseline.

Key insights

• Both `d_SW_2` and `√d_SW_1` are Hilbertian distances, allowing for the direct construction of universal positive definite kernels on the space of probability distributions.
• The theoretical framework for distance substitution kernels can be extended to provide generalized excess risk bounds for KRR estimators using SW kernels, establishing their consistency.
• Sliced Wasserstein kernels inherently capture geometric relationships between distributions more effectively than MMD, leading to improved performance in tasks sensitive to structural patterns or transformations.

Summary by alphaXiv.