Timezone: »
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)
Related Events (a corresponding poster, oral, or spotlight)
-
2018 Oral: On the Spectrum of Random Features Maps of High Dimensional Data »
Fri Jul 13th 02:00 -- 02:20 PM Room K11
More from the Same Authors
-
2019 Poster: Random Matrix Improved Covariance Estimation for a Large Class of Metrics »
Malik TIOMOKO A · Romain Couillet · Florent BOUCHARD · Guillaume GINOLHAC -
2019 Oral: Random Matrix Improved Covariance Estimation for a Large Class of Metrics »
Malik TIOMOKO A · Romain Couillet · Florent BOUCHARD · Guillaume GINOLHAC -
2018 Poster: The Dynamics of Learning: A Random Matrix Approach »
Zhenyu Liao · Romain Couillet -
2018 Oral: The Dynamics of Learning: A Random Matrix Approach »
Zhenyu Liao · Romain Couillet