PARALLELIZABLE ALGORITHMS FOR THE SELECTION OF GROUPED VARIABLES∗

Well-appreciated in statistics for its ability to select relevant grouped features (factors) in linear regression models, the group-Lasso estimator has been fruitfully applied to diverse signal processing problems including RF spectrum cartogra-phy and robust layered sensing. These applications motivate the distributed group-Lasso algorithm developed in this pa-per, that can be run by a network of wireless sensors, or, by multiple processors to balance the load of a single com-putational unit. After reformulating the group-Lasso cost into a separable form, it is iteratively minimized using the method of multipliers to obtain parallel per agent and per factor estimate updates given by vector soft-thresholding op-erations. Through affordable inter-agent communication of sparse messages, the local estimates provably consent to the global group-Lasso solution. Specializing to a single agent network, or, to univariate factors, efficient (distributed) Lasso solvers are rediscovered as a byproduct. Index Terms — Sparsity, linear regression, (group-)Lasso, parallel optimization, distributed estimation