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On the Size of the Online Kernel Sparsification Dictionary

Machine Learning 2019-08-15 v1 Machine Learning

Abstract

We analyze the size of the dictionary constructed from online kernel sparsification, using a novel formula that expresses the expected determinant of the kernel Gram matrix in terms of the eigenvalues of the covariance operator. Using this formula, we are able to connect the cardinality of the dictionary with the eigen-decay of the covariance operator. In particular, we show that under certain technical conditions, the size of the dictionary will always grow sub-linearly in the number of data points, and, as a consequence, the kernel linear regressor constructed from the resulting dictionary is consistent.

Cite

@article{arxiv.1206.4623,
  title  = {On the Size of the Online Kernel Sparsification Dictionary},
  author = {Yi Sun and Faustino Gomez and Juergen Schmidhuber},
  journal= {arXiv preprint arXiv:1206.4623},
  year   = {2019}
}

Comments

ICML2012

R2 v1 2026-06-21T21:22:46.744Z