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2017

Distributionally Robust Groupwise Regularization Estimator

Blanchet, Jose, Kang, Yang

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Regularized estimators in the context of group variables have been applied successfully in model and feature selection in order to preserve interpretability.

We formulate a Distributionally Robust Optimization (DRO) problem which recovers popular estimators, such as Group Square Root Lasso (GSRL).
Our DRO formulation allows us to interpret GSRL as a game, in which we learn a regression parameter while an adversary chooses a perturbation of the data.
We wish to pick the parameter to minimize the expected loss under any plausible model chosen by the adversary - who, on the other hand, wishes to increase the expected loss.

Distributionally Robust Groupwise Regularization Estimator · Around

Built on

Regression shrinkage and selection via the Lasso
Tibshirani, R. (1996) · 1996
Earlier work this paper cites.
Model selection and estimation in regression with grouped variables
Yuan, M. and Lin, Y. (2006) · 2006
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The group Lasso for logistic regression
Meier, L., Van De Geer, S., and Bühlmann, P. (2008) · 2008
Earlier work this paper cites.
Optimal Transport: old and new
Villani, C. (2008) · 2008
Earlier work this paper cites.
Robust regression and Lasso
Xu, H., Caramanis, C., and Mannor, S. (2009) · 2009
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