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. Copyright 2012 by the author(s)/owner(s).
|Original language||English (US)|
|Title of host publication||Proceedings of the 29th International Conference on Machine Learning, ICML 2012|
|Number of pages||8|
|State||Published - Oct 10 2012|