On the Spectrum of Random Features Maps of High Dimensional Data

Zhenyu Liao (1) , Romain Couillet (1, 2)

1 L2S - Laboratoire des signaux et systèmes
2 GIPSA-CICS - GIPSA - Communication Information and Complex Systems

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.

Domaines: Apprentissage [cs.LG]; Traitement du signal et de l'image [eess.SP]; Statistiques [math.ST]

Zhenyu Liao, Romain Couillet. On the Spectrum of Random Features Maps of High Dimensional Data. ICML 2018 - 35th International Conference on Machine Learning, Jul 2018, Stockholm, Sweden. ⟨hal-01954933⟩