The composite absolute penalties family for grouped and hierarchical variable selection

Extracting useful information from high-dimensional data is an important focus of today’s statistical research and practice. Penalized loss function minimization has been shown to be effective for this task both theoretically and empirically. With the virtues of both regularization and sparsity, the L1-penalized squared error minimization method Lasso has been popular in regression models and beyond. In this paper, we combine different norms including L1 to form an intelligent penalty in order to add side information to the fitting of a regression or classification model to obtain reasonable estimates. Specifically, we introduce the Composite Absolute Penalties (CAP) family, which allows given grouping and…

• NS
  National Science Foundation
• AC
  Adolph C. and Mary Sprague Miller Institute for Basic Research in Science, University of California Berkeley
• NN
  National Natural Science Foundation of China

  Award: 60628102
• AR
  Army Research Office

  Awards: W911NF, 911NF