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Activity Number: 504 - Model/Variable Selection
Type: Contributed
Date/Time: Wednesday, August 2, 2017 : 10:30 AM to 12:20 PM
Sponsor: Biometrics Section
Abstract #324923 View Presentation
Title: Empirical Bayes Methods for Penalized Regression: Estimation for Noisy Matrices/Tensors Without Replicates and Penalized Regression with Unknown Norm Penalty
Author(s): Maryclare Griffin* and Peter Hoff
Companies: and Duke University
Keywords: empirical Bayes ; lasso ; penalized regression ; tensor ; matrix
Abstract:

It is well known that many penalized regression problems can be interpreted as posterior mode estimation problems for a specific likelihood and prior distribution. We use the posterior mode interpretation to provide simple estimators of noise variance and unknown prior distribution parameters that can be in turn used as tuning parameters in penalized regression problems. First, we consider estimation of a mean matrix or tensor given a single noisy realization. We assume the matrix (K-way tensor) can be expressed by a 2-way (K-way) ANOVA decomposition plus possibly sparse elementwise effects. We provide a simple procedure for separately estimating the random noise variance and tuning parameter using simple functions of the observed data. Second, we consider settings where penalized regression is useful however the specific choice of penalty is not well motivated. We leverage the relationship between norm penalties and a class of prior distributions to provide (i) a statistical test of whether or not a lasso penalty is justified by the data and (ii) a simple procedure for estimating the appropriate norm and tuning parameter simultaneously.


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