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

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dc.creatorSteinwart, Ingo
dc.creatorAnghel, Marian
dc.date2007-07-02
dc.date2009-04-07
dc.date.accessioned2026-07-07T13:00:27Z
dc.date.available2026-07-07T13:00:27Z
dc.descriptionWe 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 $\mathbb{R}^d$ 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 $α$-mixing.
dc.descriptionPublished in at http://dx.doi.org/10.1214/07-AOS562 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0707.0322
dc.identifierhttp://arxiv.org/abs/0707.0322
dc.identifierAnnals of Statistics 2009, Vol. 37, No. 2, 841-875
dc.identifierdoi:10.1214/07-AOS562
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/225844
dc.subjectMethodology
dc.subjectDynamical Systems
dc.subjectStatistics Theory
dc.subject62M20 (Primary) 37D25, 37C99, 37M10, 60K99, 62M10, 62M45, 68Q32, 68T05 (Secondary)
dc.titleConsistency of support vector machines for forecasting the evolution of an unknown ergodic dynamical system from observations with unknown noise
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