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Practical selection of SVM parameters and noise estimation for SVM regression. (English) Zbl 1075.68632
Summary: We investigate practical selection of hyper-parameters for support vector machines (SVM) regression (that is, $ϵ$-insensitive zone and regularization parameter $C$). The proposed methodology advocates analytic parameter selection directly from the training data, rather than re-sampling approaches commonly used in SVM applications. In particular, we describe a new analytical prescription for setting the value of insensitive zone $ϵ$, as a function of training sample size. Good generalization performance of the proposed parameter selection is demonstrated empirically using several low- and high-dimensional regression problems. Further, we point out the importance of Vapnik’s $ϵ$-insensitive loss for regression problems with finite samples. To this end, we compare generalization performance of SVM regression (using proposed selection of $ϵ$-values) with regression using ‘least-modulus’ loss ($ϵ=0$) and standard squared loss. These comparisons indicate superior generalization performance of SVM regression under sparse sample settings, for various types of additive noise.