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Cross-Validation Optimization for Structured Hessian Kernel Methods

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Seeger,  M
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Chapelle,  O
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Seeger, M., & Chapelle, O.(2006). Cross-Validation Optimization for Structured Hessian Kernel Methods.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-D2F3-5
Abstract
We address the problem of learning hyperparameters in kernel methods for which the Hessian of the objective is structured. We propose an approximation to the cross-validation log likelihood whose gradient can be computed analytically, solving the hyperparameter learning problem efficiently through nonlinear optimization. Crucially, our learning method is based entirely on matrix-vector multiplication primitives with the kernel matrices and their derivatives, allowing straightforward specialization to new kernels or to large datasets. When applied to the problem of multi-way classification, our method scales linearly in the number of classes and gives rise to state-of-the-art results on a remote imaging task.