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Cross-Validation Optimization for Structured Hessian Kernel Methods


Technical Report


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.

Author(s): Seeger, M. and Chapelle, O.
Year: 2006
Month: February
Day: 0

Department(s): Empirical Inference
Bibtex Type: Technical Report (techreport)

Institution: Max-Planck Institute for Biological Cybernetics, Tübingen, Germany

Digital: 0
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF


  title = {Cross-Validation Optimization for Structured Hessian Kernel Methods},
  author = {Seeger, M. and Chapelle, O.},
  organization = {Max-Planck-Gesellschaft},
  institution = {Max-Planck Institute for Biological Cybernetics, Tübingen, Germany},
  school = {Biologische Kybernetik},
  month = feb,
  year = {2006},
  month_numeric = {2}