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The exclusive lasso (also known as elitist lasso) regularization has becomepopular recently due to its superior performance on structured sparsity. Itscomplex nature poses difficulties for the computation of high-dimensionalmachine learning models involving such a regularizer. In this paper, we proposean adaptive sieving (AS) strategy for generating solution paths of machinelearning models with the exclusive lasso regularizer, wherein a sequence ofreduced problems with much smaller sizes need to be solved. In order to solvethese reduced problems, we propose a highly efficient dual Newton method basedproximal point algorithm (PPDNA). As important ingredients, we systematicallystudy the proximal mapping of the weighted exclusive lasso regularizer and thecorresponding generalized Jacobian. These results also make popular first-orderalgorithms for solving exclusive lasso models practical. Various numericalexperiments for the exclusive lasso models have demonstrated the effectivenessof the AS strategy for generating solution paths and the superior performanceof the PPDNA.

Adaptive Sieving with PPDNA: Generating Solution Paths of Exclusive Lasso Models