We consider the problem of forecasting the next (observable) state of an unknown ergodic dynamical system from a noisy observation of the present state. Our main result shows, for example, that support vector machines (SVMs) using Gaussian RBF kernels can learn the best forecaster from a sequence of noisy observations if (a) the unknown observational noise process is bounded and has a summable α-mixing rate and (b) the unknown ergodic dynamical system is defined by a Lipschitz continuous function on some compact subset of ℝd and has a summable decay of correlations for Lipschitz continuous functions. In order to prove this result we first establish a general consistency result for SVMs and all stochastic processes that satisfy a mixing notion that is substantially weaker than α-mixing.
@article{1236693152,
author = {Steinwart, Ingo and Anghel, Marian},
title = {Consistency of support vector machines for forecasting the evolution of an unknown ergodic dynamical system from observations with unknown noise},
journal = {Ann. Statist.},
volume = {37},
number = {1},
year = {2009},
pages = { 841-875},
language = {en},
url = {http://dml.mathdoc.fr/item/1236693152}
}
Steinwart, Ingo; Anghel, Marian. Consistency of support vector machines for forecasting the evolution of an unknown ergodic dynamical system from observations with unknown noise. Ann. Statist., Tome 37 (2009) no. 1, pp. 841-875. http://gdmltest.u-ga.fr/item/1236693152/