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Communication dans un congrès

Pseudo-Bayesian Learning with Kernel Fourier Transform as Prior

Gaël Letarte 1 Emilie Morvant 2 Pascal Germain 3
3 MODAL - MOdel for Data Analysis and Learning
LPP - Laboratoire Paul Painlevé - UMR 8524, Université de Lille, Sciences et Technologies, Inria Lille - Nord Europe, METRICS - Evaluation des technologies de santé et des pratiques médicales - ULR 2694, Polytech Lille - École polytechnique universitaire de Lille
Abstract : We revisit Rahimi and Recht (2007)’s kernel random Fourier features (RFF) method through the lens of the PAC-Bayesian theory. While the primary goal of RFF is to approximate a kernel, we look at the Fourier transform as a prior distribution over trigonometric hypotheses. It naturally suggests learning a posterior on these hypotheses. We derive generalization bounds that are optimized by learning a pseudo-posterior obtained from a closed-form expression. Based on this study, we consider two learning strategies: The first one finds a compact landmarks-based representation of the data where each landmark is given by a distribution-tailored similarity measure, while the second one provides a PAC-Bayesian justification to the kernel alignment method of Sinha and Duchi (2016).
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Communication dans un congrès
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https://hal.archives-ouvertes.fr/hal-01908555
Contributeur : Emilie Morvant <>
Soumis le : mardi 19 février 2019 - 16:37:08
Dernière modification le : mardi 10 novembre 2020 - 11:14:06

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  • HAL Id : hal-01908555, version 2
  • ARXIV : 1810.12683

Citation

Gaël Letarte, Emilie Morvant, Pascal Germain. Pseudo-Bayesian Learning with Kernel Fourier Transform as Prior. The 22nd International Conference on Artificial Intelligence and Statistics, Apr 2019, Naha, Japan. ⟨hal-01908555v2⟩

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