2017/05/11 by José Blanchet, Blanchet, Jose, Yang Kang +1 · 2 citations
Computer Science · Decision Sciences · Mathematics · #Distributed Sensor Networks and Detection Algorithms #FOS: Mathematics #Multi-Criteria Decision Making #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1705.04241
openalex publication_date 2017/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. The regularization parameter turns out to be precisely determined by the amount of perturbation on the training data allowed by the adversary. In this paper, we introduce a data-driven (statistical) criterion for the optimal choice of regularization, which we evaluate asymptotically, in closed form, as the size of the training set increases. Our easy-to-evaluate regularization formula is compared against cross-validation, showing good (sometimes superior) performance.