| dc.contributor.advisor |
Tomaso Poggio |
en_US |
| dc.contributor.author |
De Mol, Christine |
en_US |
| dc.contributor.author |
Rosasco, Lorenzo |
en_US |
| dc.contributor.author |
De Vito, Ernesto |
en_US |
| dc.contributor.other |
Center for Biological and Computational Learning (CBCL) |
en_US |
| dc.date.accessioned |
2008-07-24T20:00:33Z |
|
| dc.date.available |
2008-07-24T20:00:33Z |
|
| dc.date.issued |
2008-07-24 |
en_US |
| dc.identifier.uri |
http://hdl.handle.net/1721.1/41889 |
|
| dc.description.abstract |
Within the framework of statistical learning theory we analyze in detail the so-called elastic-net regularization scheme proposed by Zou and Hastie ["Regularization and variable selection via the elastic net" J. R. Stat. Soc. Ser. B, 67(2):301-320, 2005] for the selection of groups of correlated variables. To investigate on the statistical properties of this scheme and in particular on its consistency properties, we set up a suitable mathematical framework. Our setting is random-design regression where we allow the response variable to be vector-valued and we consider prediction functions which are linear combination of elements (features) in an infinite-dimensional dictionary. Under the assumption that the regression function admits a sparse representation on the dictionary, we prove that there exists a particular "elastic-net representation" of the regression function such that, if the number of data increases, the elastic-net estimator is consistent not only for prediction but also for variable/feature selection. Our results include finite-sample bounds and an adaptive scheme to select the regularization parameter. Moreover, using convex analysis tools, we derive an iterative thresholding algorithm for computing the elastic-net solution which is different from the optimization procedure originally proposed in "Regularization and variable selection via the elastic net". |
en_US |
| dc.description.provenance |
Made available in DSpace on 2008-07-24T20:00:33Z (GMT). No. of bitstreams: 2
MIT-CSAIL-TR-2008-046.pdf: 462219 bytes, checksum: f13e55fc6c29d08fa9349baabf45e177 (MD5)
MIT-CSAIL-TR-2008-046.ps: 73870 bytes, checksum: 66e3aaf27a587bec086310b608cb3e4a (MD5)
Previous issue date: 2008-07-24 |
en |
| dc.description.provenance |
Submitted by CSAIL Importer (publications-dspace@csail.mit.edu) on 2008-07-24T20:00:31Z
No. of bitstreams: 2
MIT-CSAIL-TR-2008-046.pdf: 462219 bytes, checksum: f13e55fc6c29d08fa9349baabf45e177 (MD5)
MIT-CSAIL-TR-2008-046.ps: 73870 bytes, checksum: 66e3aaf27a587bec086310b608cb3e4a (MD5) |
en |
| dc.format.extent |
32 p. |
en_US |
| dc.relation.ispartofseries |
MIT-CSAIL-TR-2008-046 |
|
| dc.relation.ispartofseries |
CBCL-273 |
|
| dc.subject |
machine learning |
en_US |
| dc.subject |
regularization |
en_US |
| dc.subject |
feature selection |
en_US |
| dc.title |
Elastic-Net Regularization in Learning Theory |
en_US |
