Oral
On the Spectrum of Random Features Maps of High Dimensional Data
Zhenyu Liao · Romain Couillet

Fri Jul 13th 04:00 -- 04:20 PM @ K11

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.

Author Information

Zhenyu Liao (L2S, CentraleSupelec)

Zhenyu Liao is a second year Ph.D. student, under the supervision of Prof. [Romain Couillet](http://romaincouillet.hebfree.org/) and Prof. [Yacine Chitour](http://www.l2s.centralesupelec.fr/en/perso/yacine.chitour), with the [Signals and Statistics group](http://www.l2s.centralesupelec.fr/en/signals/presentation-signal-statistics-group) of [Laboratoire des signaux et systèmes](https://www.l2s.centralesupelec.fr/en), [CentraleSupélec](http://www.centralesupelec.fr/en), [University Paris-Saclay](https://www.universite-paris-saclay.fr/en). He received his B.Sc degree in [Optical & Electronic Information](http://english.oei.hust.edu.cn/) from [Huazhong University of Science & Technology](http://english.hust.edu.cn/), China and his M.Sc. degree in Signal and Image Processing from [CentraleSupélec](http://www.centralesupelec.fr/en)/[Paris-Sud University](http://www.u-psud.fr/en/index.html), France in 2016.

Romain Couillet (CentralSupélec)

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