The learning performance of the weak rescaled pure greedy algorithms

We investigate the regression problem in supervised learning by means of the weak rescaled pure greedy algorithm (WRPGA). We construct learning estimator by applying the WRPGA and deduce the tight upper bounds of the K -functional error estimate for the corresponding greedy learning algorithms in Hilbert spaces. Satisfactory learning rates are obtained under two prior assumptions on the regression function. The application of the WRPGA in supervised learning considerably reduces the computational cost while maintaining its powerful generalization capability when compared with other greedy learning algorithms.