B0568
Title: Support vector machines for non-i.i.d. observations
Authors: Katharina Strohriegl - University of Bayreuth (Germany) [presenting]
Andreas Christmann - University of Bayreuth (Germany)
Abstract: Today, support vector machines and other regularized kernel methods are an important tool to solve classification and regression problems. The goal of support vector machines is to find a function, which describes the relation between input values $x$ and output values $y$, by using a given data set. So far, the overwhelming part of theoretical work is done for the assumption that data are generated by independent and identically distributed random variables. However, this assumption is not fulfilled in many practical applications, and non-i.i.d. cases increasingly attract attention. We examine important properties of statistical estimators - consistency and qualitative robustness in the case of observations which do not fulfill the i.i.d. assumption. To generalize the results of the i.i.d. case we consider stochastic processes which provide a certain convergence of the empirical measure to a limiting distribution. Consistency can be shown for assumptions on the dependence structure of the stochastic process and for the assumption on the empirical measure. Examples are $\alpha$-mixing processes and weakly dependent processes. Moreover the convergence of the empirical measure together with assumptions on the estimator lead to qualitative robustness, for some processes a bootstrap approach is also qualitatively robust.
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