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On the Spectrum of Random Features Maps of High Dimensional Data

Abstract : Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration" phenomenon induced by random matrix theory to perform a spectral analysis on the Gram matrix of these random feature maps, here for Gaussian mixture models of simultaneously large dimension and size. Our results are instrumental to a deeper understanding on the interplay of the nonlinearity and the statistics of the data, thereby allowing for a better tuning of random feature-based techniques.
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https://hal.archives-ouvertes.fr/hal-01954933
Contributor : Zhenyu Liao <>
Submitted on : Friday, December 14, 2018 - 9:24:52 AM
Last modification on : Wednesday, May 20, 2020 - 1:44:13 AM

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  • HAL Id : hal-01954933, version 1
  • ARXIV : 1805.11916

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Zhenyu Liao, Romain Couillet. On the Spectrum of Random Features Maps of High Dimensional Data. International Conference on Machine Learning (ICML 2018), Jul 2018, Stockholm, Sweden. ⟨hal-01954933⟩

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