Consistency of support vector machines for forecasting the evolution of an unknown ergodic dynamical system from observations with unknown noise
Abstract
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 $\alpha$mixing rate and (b) the unknown ergodic dynamical system is defined by a Lipschitz continuous function on some compact subset of $\mathbb{R}^d$ 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 $\alpha$mixing.
 Publication:

arXiv eprints
 Pub Date:
 July 2007
 arXiv:
 arXiv:0707.0322
 Bibcode:
 2007arXiv0707.0322S
 Keywords:

 Statistics  Methodology;
 Mathematics  Dynamical Systems;
 Mathematics  Statistics;
 62M20 (Primary) 37D25;
 37C99;
 37M10;
 60K99;
 62M10;
 62M45;
 68Q32;
 68T05 (Secondary)
 EPrint:
 Published in at http://dx.doi.org/10.1214/07AOS562 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)