Likelihood Adaptive Modified Penalties and the Properties

• Activity Number: 322
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Yang Feng*+ and Tengfei Li and Zhiliang Ying
• Companies: Columbia University and Fudan University and Columbia University
• Keywords: Asymptotic stability ; Likelihood Adaptively Modified Penalties (LAMP) ; poisson penalty ; sigmoid penalty

Abstract

For variable selection, balancing sparsity and stability is a very important task. Inspired by Bayesian interpretations of penalty functions, we propose a new family of Likelihood Adaptively Modified Penalties (LAMP), where the penalty function in the family is adaptively changed with the form of the likelihood function. In addition, we introduce the notion of asymptotic stability. Two types of asymptotic stability are defined and it is shown that LAMP can achieve both types of stability while achieving oracle properties. In addition, LAMP could be seen as a special functional of a conjugate prior. An efficient coordinate-descent algorithm is proposed and a balancing method is introduced. Simulation results and real data analysis show LAMP has competitive performance comparing with several well-known penalties.