Data-driven Random Fourier Features using Stein Effect

Large-scale kernel approximation is an important problem in machine learning research. Approaches using random Fourier features have become increasingly popular \cite{Rahimi_NIPS_07}, where kernel approximation is treated as empirical mean estimation via Monte Carlo (MC) or Quasi-Monte Carlo (QMC) integration \cite{Yang_ICML_14}. A limitation of the current approaches is that all the features receive an equal weight summing to 1. In this paper, we propose a novel shrinkage estimator from "Stein effect", which provides a data-driven weighting strategy for random features and enjoys theoretical justifications in terms of lowering the empirical risk. We further present an efficient randomized algorithm for large-scale applications of the proposed method. Our empirical results on six benchmark data sets demonstrate the advantageous performance of this approach over representative baselines in both kernel approximation and supervised learning tasks.