On the size of the online kernel sparsification dictionary

Yi Sun; Faustino Gomez; Jürgen Schmidhuber

On the size of the online kernel sparsification dictionary

Yi Sun, Faustino Gomez, Jürgen Schmidhuber

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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. 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
Pages	329-336
Number of pages	8
State	Published - Oct 10 2012
Externally published	Yes

Cite this

@inproceedings{dd80b20e3cc74775b6008c537e339e82,

title = "On the size of the online kernel sparsification dictionary",

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. Copyright 2012 by the author(s)/owner(s).",

author = "Yi Sun and Faustino Gomez and J{\"u}rgen Schmidhuber",

note = "Generated from Scopus record by KAUST IRTS on 2022-09-14",

year = "2012",

month = oct,

day = "10",

language = "English (US)",

isbn = "9781450312851",

pages = "329--336",

booktitle = "Proceedings of the 29th International Conference on Machine Learning, ICML 2012",

}

TY - GEN

T1 - On the size of the online kernel sparsification dictionary

AU - Sun, Yi

AU - Gomez, Faustino

AU - Schmidhuber, Jürgen

N1 - Generated from Scopus record by KAUST IRTS on 2022-09-14

PY - 2012/10/10

Y1 - 2012/10/10

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=84867119804&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781450312851

SP - 329

EP - 336

BT - Proceedings of the 29th International Conference on Machine Learning, ICML 2012

ER -

On the size of the online kernel sparsification dictionary

Abstract

Other files and links

Fingerprint

Cite this