2015/06/08 by Youssef Mroueh, Mroueh, Youssef, Stephen Voinea +3 · 10 citations
Computer Science · Mathematics · #Artificial intelligence #Bayesian Methods and Mixture Models #Computer Vision and Pattern Recognition (cs.CV) #Computer science #Discrete mathematics #FOS: Computer and information sciences #Face and Expression Recognition #Feature vector #Hilbert space #Invariant (physics) #Kernel (algebra) #Kernel embedding of distributions #Kernel method #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematics #Neural Networks and Applications #Pattern recognition (psychology) #Polynomial kernel #Pure mathematics #Radial basis function kernel #Reproducing kernel Hilbert space #String kernel #Support vector machine #Variable kernel density estimation #cs.CV #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.1506.02544
published in arXiv (Cornell University) 28, 1558-1566 (Cornell University) · NIPS 2015
openalex publication_date 2015/06/08 · arxiv created 2015/12/04 · arxiv updated 2015/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyze in this paper a random feature map based on a theory of invariance I-theory introduced recently. More specifically, a group invariant signal signature is obtained through cumulative distributions of group transformed random projections. Our analysis bridges invariant feature learning with kernel methods, as we show that this feature map defines an expected Haar integration kernel that is invariant to the specified group action. We show how this non-linear random feature map approximates this group invariant kernel uniformly on a set of N points. Moreover, we show that it defines a function space that is dense in the equivalent Invariant Reproducing Kernel Hilbert Space. Finally, we quantify error rates of the convergence of the empirical risk minimization, as well as the reduction in the sample complexity of a learning algorithm using such an invariant representation for signal classification, in a classical supervised learning setting.