Distributed sparse linear regression

The Lasso is a popular technique for joint estimation and continuous variable selection, especially well-suited for sparse and possibly under-determined linear regression problems. This paper develops algorithms to estimate the regression coefficients via Lasso when the training data are distributed across different agents, and their communication to a central processing unit is prohibited for e.g., communication cost or privacy reasons. A motivating application is explored in the context of wireless communications, whereby sensing cognitive radios collaborate to estimate the radio-frequency power spectrum density. Attaining different tradeoffs between complexity and convergence speed, three novel algorithms are obtained after reformulating the Lasso into a separable form, which is iteratively minimized using the alternating-direction method of multipliers so as to gain the desired degree of parallelization. Interestingly, the per agent estimate updates are given by simple soft-thresho...

• Type: Journal
• Year: 2010
• Where: TSP
• Authors: Gonzalo Mateos, Juan Andrés Bazerque, Georgios B. Giannakis
• Keywords: Artificial Intelligence, Communication, Global Lasso Solution, Lasso, TSP 2010