Learning Functions of Few Arbitrary Linear Parameters in High Dimensions

Let us assume that f is a continuous function defined on the unit ball of Rd , of the form f(x) = g(Ax), where A is a k×d matrix and g is a function of k variables for k ≪ d. We are given a budget m ∈ N of possible point evaluations f(xi), i = 1, . . . , m, of f, which we are allowed to query in order to construct a uniform approximating function. Under certain smoothness and variation assumptions on the function g, and an arbitrary choice of the matrix A, we present in this paper

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Massimo Fornasier, Karin Schnass, Jan Vybíral
• Keywords: Continuous Function, CORR 2010, Education, Possible Point Evaluations, Unit Ball