Naslidnyk, Masha; Chau, Siu Lun; Briol, François-Xavier; Muandet, Krikamol; (2025) Kernel Quantile Embeddings and Associated Probability Metrics. In: Proceedings of the 42 nd International Conference on Machine Learning. PMLR: Vancouver, Canada. (In press).

Preview

Text 2505.20433v1.pdf - Published Version Download (840kB) | Preview

Abstract

Embedding probability distributions into reproducing kernel Hilbert spaces (RKHS) has enabled powerful nonparametric methods such as the maximum mean discrepancy (MMD), a statistical distance with strong theoretical and computational properties. At its core, the MMD relies on kernel mean embeddings to represent distributions as mean functions in RKHS. However, it remains unclear if the mean function is the only meaningful RKHS representation. Inspired by generalised quantiles, we introduce the notion of kernel quantile embeddings (KQEs). We then use KQEs to construct a family of distances that: (i) are probability metrics under weaker kernel conditions than MMD; (ii) recover a kernelised form of the sliced Wasserstein distance; and (iii) can be efficiently estimated with near-linear cost. Through hypothesis testing, we show that these distances offer a competitive alternative to MMD and its fast approximations.

Download activity - last month

Export as JSONXMLCSV

Download activity - last 12 months

Export as JSONXMLCSV

Downloads by country - last 12 months

Export as JSONCSVXML

Archive Staff Only

View Item