IJPAM: Volume 47, No. 4 (2008)

STATISTICAL LEARNING METHODS FOR UNIFORM
APPROXIMATION BOUNDS IN MULTIRESOLUTION SPACES

Mark A. Kon$^1$, Louise A. Raphael$^2$
$^1$Department of Mathematics and Statistics
Boston University
Boston, MA 02215, USA
e-mail: mkon@math.bu.edu
$^2$Department of Mathematics
Howard University
Washington, DC 20059, USA
e-mail: lraphael@howard.edu


Abstract.New constructive and non-constructive non-asymptotic uniform error bounds for approximating functions in $\mathcal L_s^2(\mathbb R^d), \ d \geq 1,$ by finite compactly supported multiresolution expansions are proved using approximation theoretic bounds derived from statistical learning theory.

Received: July 24, 2008

AMS Subject Classification: 41A25, 41A65, 68T05

Key Words and Phrases: statistical learning theory (SLT), VC dimension, multiresolution analysis (MRA), wavelets, reproducing kernel Hilbert space (RKHS)

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 47
Issue: 4