NDLI: Distributed Sparse Linear Regression

Content Provider	IEEE Xplore Digital Library
Author	Mateos, G. Bazerque, J.A. Giannakis, G.B.
Copyright Year	1991
Abstract	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-thresholding operations, and inter-agent communication overhead remains at affordable level. Without exchanging elements from the different training sets, the local estimates consent to the global Lasso solution, i.e., the fit that would be obtained if the entire data set were centrally available. Numerical experiments with both simulated and real data demonstrate the merits of the proposed distributed schemes, corroborating their convergence and global optimality. The ideas in this paper can be easily extended for the purpose of fitting related models in a distributed fashion, including the adaptive Lasso, elastic net, fused Lasso and nonnegative garrote.
Sponsorship	IEEE Signal Processing Society
Starting Page	5262
Ending Page	5276
Page Count	15
File Size	1053489
File Format	PDF
ISSN	1053587X
Volume Number	58
Issue Number	10
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-10-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Linear regression Input variables Training data Central Processing Unit Costs Data privacy Context Wireless communication Cognitive radio Collaboration sparse estimation Distributed linear regression Lasso parallel optimization
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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