Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
A Flexible Noise Model For Designing Maps
VMV '01 Proceedings of the Vision Modeling and Visualization Conference 2001
Database-friendly random projections: Johnson-Lindenstrauss with binary coins
Journal of Computer and System Sciences - Special issu on PODS 2001
Approximate nearest neighbors and the fast Johnson-Lindenstrauss transform
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Improved Approximation Algorithms for Large Matrices via Random Projections
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Optimal Rates for the Regularized Least-Squares Algorithm
Foundations of Computational Mathematics
Random projection trees and low dimensional manifolds
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Dense Fast Random Projections and Lean Walsh Transforms
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Compressed Spectral Clustering
ICDMW '09 Proceedings of the 2009 IEEE International Conference on Data Mining Workshops
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We investigate a method for regression that makes use of a randomly generated subspace GP ⊂ F (of finite dimension P) of a given large (possibly infinite) dimensional function space F, for example, L2([0,1]d;R). GP is defined as the span of P random features that are linear combinations of a basis functions of F weighted by random Gaussian i.i.d. coefficients. We show practical motivation for the use of this approach, detail the link that this random projections method share with RKHS and Gaussian objects theory and prove, both in deterministic and random design, approximation error bounds when searching for the best regression function in GP rather than in F, and derive excess risk bounds for a specific regression algorithm (least squares regression in GP). This paper stresses the motivation to study such methods, thus the analysis developed is kept simple for explanations purpose and leaves room for future developments.