Adaptive Shrinkage via the Hyperpenalized EM Algorithm

• Activity Number: 111
• Type: Invited
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: ASA
• Author(s): Philip S. Boonstra*+ and Bhramar Mukherjee and Jeremy Taylor
• Companies: Department of Biostatistics, University of Michigan and University of Michigan and University of Michigan
• Keywords: High-Dimensional Data ; Penalized Regression ; Ridge Regression ; Shrinkage ; Tuning Parameter Selection

Abstract

An extension of the Expectation-Maximization (EM) algorithm is the penalized EM (PEM) algorithm, which is used in missing-data problems that require maximum penalized likelihood estimates. An important element of the penalized likelihood is the choice of penalty parameter, but there is little work on choosing this parameter in a missing-data context. In this talk, we modify the PEM algorithm to simultaneously allow for automatic selection of this penalty parameter. This is called the hyperpenalized EM (HEM) algorithm. We extend the hierarchical perspective of a penalized likelihood by shrinking the penalty parameter itself with a "hyperpenalty" and estimating the penalty parameter in the algorithm. To demonstrate the approach, we analyze a gene expression dataset for predicting survival in lung cancer patients. Some observations are censored, and for some observations only matched surrogates of gene expression are available. Thus, there are two types of missing data. Further, the number of genes is large relative to the number of observations, necessitating the shrinkage of coefficients to improve prediction error.