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Communication Dans Un Congrès Année : 2022

Nyström Kernel Mean Embeddings

Résumé

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 Nystr\"om method, which exploits a small random subset of the dataset. Our main result is an upper bound on the approximation error of this procedure. It yields sufficient conditions on the subsample size to obtain the standard $n^{-1/2}$ rate while reducing computational costs. We discuss applications of this result for the approximation of the maximum mean discrepancy and quadrature rules, and illustrate our theoretical findings with numerical experiments.

Dates et versions

hal-04510239 , version 1 (18-03-2024)

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Antoine Chatalic, Nicolas Schreuder, Alessandro Rudi, Lorenzo Rosasco. Nyström Kernel Mean Embeddings. ICML 2022 - 39th International Conference on Machine Learning, Jul 2022, Baltimore, United States. ⟨hal-04510239⟩
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