2004, Vol.7, No.4, pp.314-331

Kernel methods such as support vector machines and other sparse approximation techniques are reviewed with an emphasis on application to random processes. Some of the kernel properties are highlighted and space dimensionality reduction approaches that are conceptually simple and computationally feasible are proposed. The stochastic analysis of random phenomena is often performed in a context characterized by non-standard probabilistic assumptions, far for instance from stationarity and Gaussianity. Real-life applications require statistical model conditions such as strong forms of dependence, non-stationarity, non-gaussianity; these features often prevent from using classical statistical inference procedures or model-building strategies, and instead involve computational techniques relying on simulations and numerical approximation. One of the problems here investigated is how to cast these methodological instruments in a comprehensive theoretical framework, and then achieve a suitable model derivation and interpretation strategy. This contribution is of an introductory nature and suggests directions for further advances targeted to real applications, in particular when time series are studied.
Key words: random processes, reproducing kernel Hilbert spaces; integral equations, support vector machines, sparse approximation techniques, wavelets and frames, model selection

Full text:  Acrobat PDF  (2336KB)   PostScript (400KB)   PostScript.gz (187KB)

Copyright © Nonlinear Phenomena in Complex Systems. Last updated: December 21, 2004