A Unified Robust Regression Model for Lasso-like Algorithms

Wenzhuo Yang, Huan Xu
Proceedings of the 30th International Conference on Machine Learning, PMLR 28(3):585-593, 2013.

Abstract

We develop a unified robust linear regression model and show that it is equivalent to a general regularization framework to encourage sparse-like structure that contains group Lasso and fused Lasso as specific examples. This provides a robustness interpretation of these widely applied Lasso-like algorithms, and allows us to construct novel generalizations of Lasso-like algorithms by considering different uncertainty sets. Using this robustness interpretation, we present new sparsity results, and establish the statistical consistency of the proposed regularized linear regression. This work extends a classical result from Xu et al. (2010) that relates standard Lasso with robust linear regression to learning problems with more general sparse-like structures, and provides new robustness-based tools to to understand learning problems with sparse-like structures.

Cite this Paper

BibTeX
@InProceedings{pmlr-v28-yang13e, title = {A Unified Robust Regression Model for Lasso-like Algorithms}, author = {Yang, Wenzhuo and Xu, Huan}, booktitle = {Proceedings of the 30th International Conference on Machine Learning}, pages = {585--593}, year = {2013}, editor = {Dasgupta, Sanjoy and McAllester, David}, volume = {28}, number = {3}, series = {Proceedings of Machine Learning Research}, address = {Atlanta, Georgia, USA}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v28/yang13e.pdf}, url = {https://proceedings.mlr.press/v28/yang13e.html}, abstract = {We develop a unified robust linear regression model and show that it is equivalent to a general regularization framework to encourage sparse-like structure that contains group Lasso and fused Lasso as specific examples. This provides a robustness interpretation of these widely applied Lasso-like algorithms, and allows us to construct novel generalizations of Lasso-like algorithms by considering different uncertainty sets. Using this robustness interpretation, we present new sparsity results, and establish the statistical consistency of the proposed regularized linear regression. This work extends a classical result from Xu et al. (2010) that relates standard Lasso with robust linear regression to learning problems with more general sparse-like structures, and provides new robustness-based tools to to understand learning problems with sparse-like structures.} }
Endnote
%0 Conference Paper %T A Unified Robust Regression Model for Lasso-like Algorithms %A Wenzhuo Yang %A Huan Xu %B Proceedings of the 30th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2013 %E Sanjoy Dasgupta %E David McAllester %F pmlr-v28-yang13e %I PMLR %P 585--593 %U https://proceedings.mlr.press/v28/yang13e.html %V 28 %N 3 %X We develop a unified robust linear regression model and show that it is equivalent to a general regularization framework to encourage sparse-like structure that contains group Lasso and fused Lasso as specific examples. This provides a robustness interpretation of these widely applied Lasso-like algorithms, and allows us to construct novel generalizations of Lasso-like algorithms by considering different uncertainty sets. Using this robustness interpretation, we present new sparsity results, and establish the statistical consistency of the proposed regularized linear regression. This work extends a classical result from Xu et al. (2010) that relates standard Lasso with robust linear regression to learning problems with more general sparse-like structures, and provides new robustness-based tools to to understand learning problems with sparse-like structures.
RIS
TY - CPAPER TI - A Unified Robust Regression Model for Lasso-like Algorithms AU - Wenzhuo Yang AU - Huan Xu BT - Proceedings of the 30th International Conference on Machine Learning DA - 2013/05/26 ED - Sanjoy Dasgupta ED - David McAllester ID - pmlr-v28-yang13e PB - PMLR DP - Proceedings of Machine Learning Research VL - 28 IS - 3 SP - 585 EP - 593 L1 - http://proceedings.mlr.press/v28/yang13e.pdf UR - https://proceedings.mlr.press/v28/yang13e.html AB - We develop a unified robust linear regression model and show that it is equivalent to a general regularization framework to encourage sparse-like structure that contains group Lasso and fused Lasso as specific examples. This provides a robustness interpretation of these widely applied Lasso-like algorithms, and allows us to construct novel generalizations of Lasso-like algorithms by considering different uncertainty sets. Using this robustness interpretation, we present new sparsity results, and establish the statistical consistency of the proposed regularized linear regression. This work extends a classical result from Xu et al. (2010) that relates standard Lasso with robust linear regression to learning problems with more general sparse-like structures, and provides new robustness-based tools to to understand learning problems with sparse-like structures. ER -
APA
Yang, W. & Xu, H.. (2013). A Unified Robust Regression Model for Lasso-like Algorithms. Proceedings of the 30th International Conference on Machine Learning, in Proceedings of Machine Learning Research 28(3):585-593 Available from https://proceedings.mlr.press/v28/yang13e.html.

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