TY  - INPR
A1  - Blanchard, Gilles
A1  - Krämer, Nicole
T1  - Convergence rates of kernel conjugate gradient for random design regression
N2  - We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is related to Kernel Partial Least Squares, a regression method that combines supervised dimensionality reduction with least squares projection. Following the setting introduced in earlier related literature, we study so-called "fast convergence rates" depending on the regularity of the target regression function (measured by a source condition in terms of the kernel integral operator) and on the effective dimensionality of the data mapped into the kernel space. We obtain upper bounds, essentially matching known minimax lower bounds, for the L^2 (prediction) norm as well as for the stronger Hilbert norm, if the true
regression function belongs to the reproducing kernel Hilbert space. If the latter assumption is not fulfilled, we obtain similar convergence rates for appropriate norms, provided additional unlabeled data are available.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016) 8 
KW  - nonparametric regression
KW  - reproducing kernel Hilbert space
KW  - conjugate gradient
KW  - partial least squares
KW  - minimax convergence rates
Y1  - 2016
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-94195
SN  - 2193-6943
VL  - 5
IS  - 8
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Blanchard, Gilles
A1  - Kraemer, Nicole
T1  - Convergence rates of Kernel Conjugate Gradient for random design regression
JF  - Analysis and applications
N2  - We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient (CG) algorithm, where regularization against over-fitting is obtained by early stopping. This method is related to Kernel Partial Least Squares, a regression method that combines supervised dimensionality reduction with least squares projection. Following the setting introduced in earlier related literature, we study so-called "fast convergence rates" depending on the regularity of the target regression function (measured by a source condition in terms of the kernel integral operator) and on the effective dimensionality of the data mapped into the kernel space. We obtain upper bounds, essentially matching known minimax lower bounds, for the L-2 (prediction) norm as well as for the stronger Hilbert norm, if the true regression function belongs to the reproducing kernel Hilbert space. If the latter assumption is not fulfilled, we obtain similar convergence rates for appropriate norms, provided additional unlabeled data are available.
KW  - Nonparametric regression
KW  - reproducing kernel Hilbert space
KW  - conjugate gradient
KW  - partial least squares
KW  - minimax convergence rates
Y1  - 2016
U6  - https://doi.org/10.1142/S0219530516400017
SN  - 0219-5305
SN  - 1793-6861
VL  - 14
SP  - 763
EP  - 794
PB  - World Scientific
CY  - Singapore
ER  -