Efficient hypothesis testing strategies for latent group lasso problem

A hypothesis testing based pre-processing procedure is proposed in this paper to reduce the computational complexity of latent group lasso (LGL) problem. The redundant overlapping support groups can be efficiently pruned while the desired groups are kept at a guaranteed rate. Three different schemes of hypothesis testing are theoretically studied and empirically compared in terms of complexity reduction, pruning accuracy, and recovery error. Of possible independent interest, the optimal designs of test statistics are also pursued to make explicit use of different signal structural priors. The theoretical claims are demonstrated via extensive numerical experiments under different settings and the proposed pre-processing procedure exhibits obvious empirical superiority in the concerned aspects.