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April 2009 Consistency of support vector machines for forecasting the evolution of an unknown ergodic dynamical system from observations with unknown noise
Ingo Steinwart, Marian Anghel
Ann. Statist. 37(2): 841-875 (April 2009). DOI: 10.1214/07-AOS562

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.

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Ingo Steinwart. Marian Anghel. "Consistency of support vector machines for forecasting the evolution of an unknown ergodic dynamical system from observations with unknown noise." Ann. Statist. 37 (2) 841 - 875, April 2009. https://doi.org/10.1214/07-AOS562

Information

Published: April 2009
First available in Project Euclid: 10 March 2009

zbMATH: 1162.62089
MathSciNet: MR2502653
Digital Object Identifier: 10.1214/07-AOS562

Subjects:
Primary: 62M20
Secondary: 37C99, 37D25, 37M10, 60K99, 62M10, 62M45, 68Q32, 68T05

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 2 • April 2009
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