Statistical Seminar: Every Monday at 2:00 pm.
Time: 2:00 pm – 3:15 pm
Date: 27th May 2024
Place: Room 3001

Nicolas Schreuder (CNRS, Université Gustave Eiffel) – Efficient estimation of kernel mean embeddings

Abstract:

Kernel mean embeddings are a powerful tool to represent probability distributions over arbitrary spaces as single points in a Hilbert space. Yet, the cost of computing and storing such embeddings prohibits their direct use in large-scale settings. We propose an efficient approximation procedure based on the Nyström method, which exploits a small random subset of the dataset. Our main result is an upper bound on the approximation error of this procedure for different sub-sampling strategies. We discuss applications of this result for numerical integration and approximation of the maximum mean discrepancy.

The talk is based on the works :

– A. Chatalic, N. Schreuder, A. Rudi, L. Rosasco (2022). Nyström Kernel Mean Embeddings. ICML 2022. [PMLR 162:3006-3024] – A. Chatalic, N. Schreuder, E. De Vito, L. Rosasco (2023). Efficient Numerical Integration in Reproducing Kernel Hilbert Spaces via Leverage Scores Sampling. [arXiv:2311.13548]

Organizers:
Anna KORBA (CREST), Karim LOUNICI (CMAP) , Jaouad MOURTADA (CREST)
Sponsors:
CREST-CMAP