Exploiting Covariate Similarity in Sparse Regression via the Pairwise Elastic Net

Alexander Lorbert, David Eis, Victoria Kostina, David Blei, Peter Ramadge
Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:477-484, 2010.

Abstract

A new approach to regression regularization called the Pairwise Elastic Net is proposed. Like the Elastic Net, it simultaneously performs automatic variable selection and continuous shrinkage. In addition, the Pairwise Elastic Net encourages the grouping of strongly correlated predictors based on a pairwise similarity measure. We give examples of how the Pairwise Elastic Net can be used to achieve the objectives of Ridge regression, the Lasso, the Elastic Net, and Group Lasso. Finally, we present a coordinate descent algorithm to solve the Pairwise Elastic Net.

Cite this Paper

BibTeX
@InProceedings{pmlr-v9-lorbert10b, title = {Exploiting Covariate Similarity in Sparse Regression via the Pairwise Elastic Net}, author = {Lorbert, Alexander and Eis, David and Kostina, Victoria and Blei, David and Ramadge, Peter}, booktitle = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics}, pages = {477--484}, year = {2010}, editor = {Teh, Yee Whye and Titterington, Mike}, volume = {9}, series = {Proceedings of Machine Learning Research}, address = {Chia Laguna Resort, Sardinia, Italy}, month = {13--15 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v9/lorbert10b/lorbert10b.pdf}, url = {https://proceedings.mlr.press/v9/lorbert10b.html}, abstract = {A new approach to regression regularization called the Pairwise Elastic Net is proposed. Like the Elastic Net, it simultaneously performs automatic variable selection and continuous shrinkage. In addition, the Pairwise Elastic Net encourages the grouping of strongly correlated predictors based on a pairwise similarity measure. We give examples of how the Pairwise Elastic Net can be used to achieve the objectives of Ridge regression, the Lasso, the Elastic Net, and Group Lasso. Finally, we present a coordinate descent algorithm to solve the Pairwise Elastic Net.} }
Endnote
%0 Conference Paper %T Exploiting Covariate Similarity in Sparse Regression via the Pairwise Elastic Net %A Alexander Lorbert %A David Eis %A Victoria Kostina %A David Blei %A Peter Ramadge %B Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2010 %E Yee Whye Teh %E Mike Titterington %F pmlr-v9-lorbert10b %I PMLR %P 477--484 %U https://proceedings.mlr.press/v9/lorbert10b.html %V 9 %X A new approach to regression regularization called the Pairwise Elastic Net is proposed. Like the Elastic Net, it simultaneously performs automatic variable selection and continuous shrinkage. In addition, the Pairwise Elastic Net encourages the grouping of strongly correlated predictors based on a pairwise similarity measure. We give examples of how the Pairwise Elastic Net can be used to achieve the objectives of Ridge regression, the Lasso, the Elastic Net, and Group Lasso. Finally, we present a coordinate descent algorithm to solve the Pairwise Elastic Net.
RIS
TY - CPAPER TI - Exploiting Covariate Similarity in Sparse Regression via the Pairwise Elastic Net AU - Alexander Lorbert AU - David Eis AU - Victoria Kostina AU - David Blei AU - Peter Ramadge BT - Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics DA - 2010/03/31 ED - Yee Whye Teh ED - Mike Titterington ID - pmlr-v9-lorbert10b PB - PMLR DP - Proceedings of Machine Learning Research VL - 9 SP - 477 EP - 484 L1 - http://proceedings.mlr.press/v9/lorbert10b/lorbert10b.pdf UR - https://proceedings.mlr.press/v9/lorbert10b.html AB - A new approach to regression regularization called the Pairwise Elastic Net is proposed. Like the Elastic Net, it simultaneously performs automatic variable selection and continuous shrinkage. In addition, the Pairwise Elastic Net encourages the grouping of strongly correlated predictors based on a pairwise similarity measure. We give examples of how the Pairwise Elastic Net can be used to achieve the objectives of Ridge regression, the Lasso, the Elastic Net, and Group Lasso. Finally, we present a coordinate descent algorithm to solve the Pairwise Elastic Net. ER -
APA
Lorbert, A., Eis, D., Kostina, V., Blei, D. & Ramadge, P.. (2010). Exploiting Covariate Similarity in Sparse Regression via the Pairwise Elastic Net. Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 9:477-484 Available from https://proceedings.mlr.press/v9/lorbert10b.html.

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