On the Size of the Online Kernel Sparsification Dictionary
Abstract
We analyze the size of the dictionary constructed from online kernel sparsi_cation, 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 sublinearly in the number of data points, and, as a consequence, the kernel linear regressor constructed from the resulting dictionary is consistent.
Cite
Text
Sun et al. "On the Size of the Online Kernel Sparsification Dictionary." International Conference on Machine Learning, 2012.Markdown
[Sun et al. "On the Size of the Online Kernel Sparsification Dictionary." International Conference on Machine Learning, 2012.](https://mlanthology.org/icml/2012/sun2012icml-size/)BibTeX
@inproceedings{sun2012icml-size,
title = {{On the Size of the Online Kernel Sparsification Dictionary}},
author = {Sun, Yi and Gomez, Faustino J. and Schmidhuber, Jürgen},
booktitle = {International Conference on Machine Learning},
year = {2012},
url = {https://mlanthology.org/icml/2012/sun2012icml-size/}
}