Kernel Quantile Embeddings and Associated Probability Metrics

Add to your list(s) Download to your calendar using vCal

• Masha Naslidnyk (University College London)
• Tuesday 06 May 2025, 15:30-16:00
• Seminar Room 1, Newton Institute.

If you have a question about this talk, please contact nobody.

RCLW01 - Uncertainty in multivariate, non-Euclidean, and functional spaces: theory and practice

Embedding probability distributions into reproducing kernel Hilbert spaces (RKHS) has enabled powerful non-parametric 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 (KMEs) 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), along with a consistent estimator. 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. Our findings demonstrate the value of representing distributions in Hilbert space beyond simple mean functions, paving the way for new avenues of research.

This talk is part of the Isaac Newton Institute Seminar Series series.

This talk is included in these lists:

• All CMS events
• Featured lists
• INI info aggregator
• Isaac Newton Institute Seminar Series
• School of Physical Sciences
• Seminar Room 1, Newton Institute
• bld31

Note that ex-directory lists are not shown.