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Abstract:
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While support vector and kernel methods have been successfully applied, there are still open questions regarding model selection. Here, we consider the problem of model selection for support vector classification and regression through cross-validation formulated as a bilevel program. This allows for versatility in handling several machine-learning goals simultaneously and efficiently: optimal choice of model parameters, feature selection for dimensionality reduction, and kernelization to handle nonlinear datasets.The bilevel formulation is converted to a mathematical program with equilibrium constraints (MPECs). Unlike SVMs, which are convex problems, the resulting problem is nonconvex. We discuss how these challenges can be solved using decomposition and successive linearization and present results.
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