Consistency of support vector machines for forecasting the evolution of an unknown ergodic dynamical system from observations with unknown noise

Details Consistency of support vector machines for forecasting the evolution of an unknown ergodic dynamical system from observations with unknown noise Consistency of support vector machines for forecasting the evolution of an unknown ergodic dynamical system from observations with unknown noise

2007-07-02

arxiv.org/abs/0707.0322v2

Annals of Statistics 2009, Vol. 37, No. 2, 841-875

Statistics

Methodology

Published in at http://dx.doi.org/10.1214/07-AOS562 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/07-AOS562

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.

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