Consistency of support vector machines for forecasting the evolution of an unknown ergodic dynamical system from observations with unknown noise
The Annals of Statistics · 2009 · Volume 37 · Issue 2
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 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.
Keywords
37C99, 37D25, 37M10, 60K99, 62M10, 62M20, 62M45, 68Q32, 68T05, consistency, forecasting dynamical systems, Observational noise model, Support vector machines
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