We derive a divergence formula for a group of regularization methods with an
L2 constraint. The formula is useful for regularization parameter selection,
because it provides an unbiased estimate for the number of degrees of freedom.
We begin with deriving the formula for smoothing splines and then extend it to
other settings such as penalized splines, ridge regression, and functional
linear regression.
%0 Journal Article
%1 Fang2012Divergence
%A Fang, Yixin
%A Wang, Yuanjia
%A Huang, Xin
%D 2012
%K statistics
%T A divergence formula for regularization methods with an L2 constraint
%U http://arxiv.org/abs/1203.3559
%X We derive a divergence formula for a group of regularization methods with an
L2 constraint. The formula is useful for regularization parameter selection,
because it provides an unbiased estimate for the number of degrees of freedom.
We begin with deriving the formula for smoothing splines and then extend it to
other settings such as penalized splines, ridge regression, and functional
linear regression.
@article{Fang2012Divergence,
abstract = {{We derive a divergence formula for a group of regularization methods with an
L2 constraint. The formula is useful for regularization parameter selection,
because it provides an unbiased estimate for the number of degrees of freedom.
We begin with deriving the formula for smoothing splines and then extend it to
other settings such as penalized splines, ridge regression, and functional
linear regression.}},
added-at = {2019-02-23T22:09:48.000+0100},
archiveprefix = {arXiv},
author = {Fang, Yixin and Wang, Yuanjia and Huang, Xin},
biburl = {https://www.bibsonomy.org/bibtex/285275bf146e6d0e45bd3a49a8bd476d3/cmcneile},
citeulike-article-id = {10476214},
citeulike-linkout-0 = {http://arxiv.org/abs/1203.3559},
citeulike-linkout-1 = {http://arxiv.org/pdf/1203.3559},
day = 15,
eprint = {1203.3559},
interhash = {0548c898c30bd89e2f8d759619e770d0},
intrahash = {85275bf146e6d0e45bd3a49a8bd476d3},
keywords = {statistics},
month = mar,
posted-at = {2012-06-16 14:00:24},
priority = {2},
timestamp = {2019-02-23T22:15:27.000+0100},
title = {{A divergence formula for regularization methods with an L2 constraint}},
url = {http://arxiv.org/abs/1203.3559},
year = 2012
}