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Activity Number: 39
Type: Contributed
Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Learning and Data Mining
Abstract #312448 View Presentation
Title: Adaptive Monotone Shrinkage for Regression
Author(s): Zhuang Ma*+ and Dean Foster and Robert Stine
Companies: Wharton School and University of Pennsylvania and University of Pennsylvania
Keywords: monotone shrinkage ; maximum marginal likelihood ; pool-adjacent-violators ; Stein's unbiased risk estimate ; oracle properties ; robustness
Abstract:

We develop an adaptive monotone shrinkage estimator for regression models with the following characteristics: i) dense coefficients with small but important effects; ii) a priori ordering that indicates the probable predictive importance of the features. We capture both properties with an empirical Bayes estimator that shrinks coefficients monotonically with respect to their anticipated importance. This estimator can be rapidly computed using a version of Pool-Adjacent-Violators algorithm. We show that the proposed monotone shrinkage approach is competitive with the class of all Bayesian estimators that share the prior information. We further observe that the estimator also minimizes Stein's unbiased risk estimate. Along with our key result that the estimator mimics the oracle Bayes rule under an order assumption, we also prove that the estimator is robust. Even without the order assumption, our estimator mimics the best performance of a large family of estimators that includes the least squares estimator, ridge estimator, James-Stein estimator, etc. Simulation results and data analysis from a model for text processing are provided to support the theory.


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