Compressed learning of high-dimensional sparse functions

This paper presents a simple randomised algorithm for recovering high-dimensional sparse functions, i.e. functions f : [0, 1]d → R which depend effectively only on k out of d variables, meaning f(x1, . . . , xd) = g(xi1 , . . . , xik ), where the indices 1 ≤ i1 < i2 < · · · < ik ≤ d are unknown. It is shown that (under certain conditions on g) this algorithm recovers the k unknown coordinates with probability at least 1−6 exp(−L) using only O(k(L+log k)(L+log d)) samples of f.

• Type: Journal
• Year: 2011
• Where: ICASSP
• Authors: Karin Schnass, Jan Vybíral
• Keywords: Certain Conditions, ICASSP 2011, Signal Processing, Simple Randomised Algorithm, Sparse