Space alternating penalized Kullback proximal point algorithms for maximizing likelihood with nondifferentiable penalty

作者：Chretien Stephane^*; Hero Alfred; Perdry Herve

来源：Annals of the Institute of Statistical Mathematics, 2012, 64(4): 791-809.

DOI：10.1007/s10463-011-0333-x

• EM algorithm
• Maximum likelihood estimation
• Sparsity
• Model selection
• Space alternating algorithm
• Nonsmooth penalty

The EM algorithm is a widely used methodology for penalized likelihood estimation. Provable monotonicity and convergence are the hallmarks of the EM algorithm and these properties are well established for smooth likelihood and smooth penalty functions. However, many relaxed versions of variable selection penalties are not smooth. In this paper, we introduce a new class of space alternating penalized Kullback proximal extensions of the EM algorithm for nonsmooth likelihood inference. We show that the cluster points of the new method are stationary points even when they lie on the boundary of the parameter set. We illustrate the new class of algorithms for the problems of model selection for finite mixtures of regression and of sparse image reconstruction.

• 出版日期2012-8