The ninety-third UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, January 8, 2026.
2–3 PM — Masha Naslidnyk (Department of Statistical Science, University College London)
Kernel Quantile Embeddings and Associated Probability Metrics
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.
References:
Joint work with Siu Lun Chau (NTU, Singapore) & François-Xavier Briol (UCL) & Krikamol Muandet (CISPA Helmholtz Center for Information Security).
Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).
Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)
Practical details: the seminar will be held online using Microsoft Teams.
If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).
You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.
The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.
