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

Fri Jul 13 07:00 AM -- 07:20 AM (PDT) @ 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 received his Ph.D. in applied math and informatics in 2019 from University of Paris-Saclay, France. In 2020 he was a postdoctoral researcher with the Department of Statistics, University of California, Berkeley. He is currently an assistant professor at Huazhong University of Science and Technology (HUST), China. His research interests are broadly in machine learning, signal processing, random matrix theory, and high-dimensional statistics. He published more than 20 papers on top-tier machine learning conferences such as ICML, NeurIPS, ICLR, COLT, AISTATS, etc., and he co-authored the book “Random Matrix Methods for Machine Learning.”

Romain Couillet (CentralSupélec)

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