TY  - JOUR
A1  - Blanchard, Gilles
A1  - Zadorozhnyi, Oleksandr
T1  - Concentration of weakly dependent Banach-valued sums and applications to statistical learning methods
JF  - Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability
N2  - We obtain a Bernstein-type inequality for sums of Banach-valued random variables satisfying a weak dependence assumption of general type and under certain smoothness assumptions of the underlying Banach norm. We use this inequality in order to investigate in the asymptotical regime the error upper bounds for the broad family of spectral regularization methods for reproducing kernel decision rules, when trained on a sample coming from a tau-mixing process.
KW  - Banach-valued process
KW  - Bernstein inequality
KW  - concentration
KW  - spectral regularization
KW  - weak dependence
Y1  - 2019
U6  - https://doi.org/10.3150/18-BEJ1095
SN  - 1350-7265
SN  - 1573-9759
VL  - 25
IS  - 4B
SP  - 3421
EP  - 3458
PB  - International Statistical Institute
CY  - Voorburg
ER  -