Local Support Vector Machines:Formulation and Analysis

09/14/2013

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by   Ravi Ganti, et al.

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We provide a formulation for Local Support Vector Machines (LSVMs) that generalizes previous formulations, and brings out the explicit connections to local polynomial learning used in nonparametric estimation literature. We investigate the simplest type of LSVMs called Local Linear Support Vector Machines (LLSVMs). For the first time we establish conditions under which LLSVMs make Bayes consistent predictions at each test point x_0. We also establish rates at which the local risk of LLSVMs converges to the minimum value of expected local risk at each point x_0. Using stability arguments we establish generalization error bounds for LLSVMs.