CONSISTENCY OF SUPPORT VECTOR MACHINES FOR FORECASTING THE EVOLUTION OF AN UNKNOWN ERGODIC DYNAMICAL SYSTEM FROM OBSERVATIONS WITH UNKNOWN NOISE

• 成果类型: Article
• 署名作者: Steinwart, Ingo; Anghel, Marian
• 署名单位: United States Department of Energy (DOE); Los Alamos National Laboratory
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS562
• 发表日期: 2009
• 页码: 841-875
• 关键词: reduction; CLASSIFICATION; regression; prediction

摘要

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 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.