Solving Fused Group Lasso Problems via Block-Splitting Algorithms

• Activity Number: 696
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Tso-Jung Yen*
• Companies: Institute of Statistical Science, Academia Sinica
• Keywords: Euclidean distance ; fused lasso ; group lasso ; alternating direction method of multipliers ; block splitting algorithms

Abstract

In this paper we propose a distributed optimization-based method for solving the fused group lasso problem, in which the penalty function is a sum of Euclidean distances between pairs of parameter vectors. As a result of that, the corresponding augmented Lagrangian will have a coupling quadratic term that is not separable in terms of these parameter vectors. We introduce a set of equality constraints that connect each parameter vector to a group of paired auxiliary variables. Under this setting, we are able to derive a modified augmented Lagrangian that is separable either in terms of the parameter vectors or in terms of the paired auxiliary variables. We develop a parallel algorithm and evaluate it by carrying out fused group lasso estimation for regression models using simulated data sets. Our results show that the parallel algorithm has a massive advantage over its non-parallel counterpart in terms of computational time and memory usage. In addition, with additional steps in each iteration, the parallel algorithm can obtain parameter values almost identical to those obtained by the non-parallel algorithm.