The Annals of Statistics
- Ann. Statist.
- Volume 37, Number 2 (2009), 841-875.
Consistency of support vector machines for forecasting the evolution of an unknown ergodic dynamical system from observations with unknown noise
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.
Ann. Statist., Volume 37, Number 2 (2009), 841-875.
First available in Project Euclid: 10 March 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]
Secondary: 37D25: Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) 37C99: None of the above, but in this section 37M10: Time series analysis 60K99: None of the above, but in this section 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62M45: Neural nets and related approaches 68Q32: Computational learning theory [See also 68T05] 68T05: Learning and adaptive systems [See also 68Q32, 91E40]
Steinwart, Ingo; Anghel, Marian. Consistency of support vector machines for forecasting the evolution of an unknown ergodic dynamical system from observations with unknown noise. Ann. Statist. 37 (2009), no. 2, 841--875. doi:10.1214/07-AOS562. https://projecteuclid.org/euclid.aos/1236693152