Abstract
This paper presents a computation of the V γ dimension for regression in bounded subspaces of Reproducing Kernel Hilbert Spaces (RKHS) for the Support Vector Machine (SVM) regression ε-insensitive loss function L ε, and general L p loss functions. Finiteness of the V γ dimension is shown, which also proves uniform convergence in probability for regression machines in RKHS subspaces that use the L ε or general L p loss functions. This paper presents a novel proof of this result. It also presents a computation of an upper bound of the V γ dimension under some conditions, that leads to an approach for the estimation of the empirical V γ dimension given a set of training data.
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Evgeniou, T., Pontil, M. (1999). On the V γ Dimension for Regression in Reproducing Kernel Hilbert Spaces. In: Watanabe, O., Yokomori, T. (eds) Algorithmic Learning Theory. ALT 1999. Lecture Notes in Computer Science(), vol 1720. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46769-6_9
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DOI: https://doi.org/10.1007/3-540-46769-6_9
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