Distributed Sparse Linear Regression

Mateos, Gonzalo; Bazerque, Juan Andrés; Giannakis, Georgios B.

doi:10.1109/tsp.2010.2055862

Cited by 465 publications

(458 citation statements)

References 32 publications

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“…Distributed compressed sensing using convex optimization is addressed in [6], [7]. Using alternating-direction-method-of-multipliers (ADMM), distributed basis pursuit [8] and distributed LASSO (D-LASSO) [9] were realized. D-LASSO is shown to solve the exact convex optimization problem of a centralized scenario in a distributed fashion.…”

Section: A Relation To Prior Workmentioning

confidence: 99%

Distributed greedy sparse learning over doubly stochastic networks

Zaki

Venkitaraman

Chatterjee

et al. 2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-In this paper, we develop a greedy algorithm for sparse learning over a doubly stochastic network. In the proposed algorithm, nodes of the network perform sparse learning by exchanging their individual intermediate variables. The algorithm is iterative in nature. We provide a restricted isometry property (RIP)-based theoretical guarantee both on the performance of the algorithm and the number of iterations required for convergence. Using simulations, we show that the proposed algorithm provides good performance.

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Section: A Relation To Prior Workmentioning

confidence: 99%

Distributed greedy sparse learning over doubly stochastic networks

Zaki

Venkitaraman

Chatterjee

et al. 2017

2017 25th European Signal Processing Conference (EUSIPCO)

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“…In addition to distributed gradient-like methods, a different type of methods -distributed (augmented) Lagrangian and distributed alternating direction of multipliers methods (ADMM) have been studied, e.g., in [10], [29]- [35]. They have in general more complex iterations than gradient methods, but may have a lower total communication cost, e.g., [30].…”

Section: Brief Comment On the Literaturementioning

confidence: 99%

“…Algorithm D-NG: Node maintains its solution estimate and an auxiliary variable , It uses arbitrary initialization and, for , performs the updates (9) (10) In (9)- (10), is the neighborhood of node (including node ). For the step-size is: (11) and is the sequence from the centralized Nesterov gradient method, [38]: (12) The D-NG algorithm works as follows.…”

Section: Algorithms D-ng and D-nc For Static Networkmentioning

confidence: 99%

“…Each of the three example problems obeys the Assumptions that we make on the 's (see ahead Assumptions 3, 4, and 5 for details.) Besides those, existing literature provides many other application examples, including distributed estimation, e.g., [4]- [6], distributed detection, e.g., [7], [8], target localization and intruder detection in biological networks, e.g., [9], and spectrum sensing for cognitive radio networks, e.g., [10].…”

Section: Introductionmentioning

confidence: 99%

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Convergence Rates of Distributed Nesterov-Like Gradient Methods on Random Networks

Jakovetić

Xavier²,

Moura

2014

IEEE Trans. Signal Process.

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Abstract-We consider distributed optimization in random networks where nodes cooperatively minimize the sum of their individual convex costs. Existing literature proposes distributed gradient-like methods that are computationally cheap and resilient to link failures, but have slow convergence rates. In this paper, we propose accelerated distributed gradient methods that 1) are resilient to link failures; 2) computationally cheap; and 3) improve convergence rates over other gradient methods. We model the network by a sequence of independent, identically distributed random matrices drawn from the set of symmetric, stochastic matrices with positive diagonals. The network is connected on average and the cost functions are convex, differentiable, with Lipschitz continuous and bounded gradients. We design two distributed Nesterov-like gradient methods that modify the D-NG and D-NC methods that we proposed for static networks. We prove their convergence rates in terms of the expected optimality gap at the cost function. Let and be the number of per-node gradient evaluations and per-node communications, respectively. Then the modified D-NG achieves rates and , and the modified D-NC rates and , where is arbitrarily small. For comparison, the standard distributed gradient method cannot do better than and , on the same class of cost functions (even for static networks). Simulation examples illustrate our analytical findings.

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“…As a result the complexity and resource consumption will be reduced, and distributed estimation is more flexible and robust to node and/or link failure [2], [3]. Recently, many distributed estimation algorithms have been proposed, such as distributed recursive least square (RLS) [4], distributed least-mean square (LMS) [5], distributed sparse estimation [6], [7], distributed expectation maximization (EM) algorithm [8], distributed Gaussian process regression [9], and distributed variational Bayesian (VB) algorithm [10].…”

Section: Introductionmentioning

confidence: 99%

A Mobile Agent Based Distributed Variational Bayesian Algorithm for Flow and Speed Estimation in a Traffic System

Mozaffari

Safarinejadian

2016

IEICE Trans. Inf. & Syst.

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SUMMARYThis paper provides a mobile agent based distributed variational Bayesian (MABDVB) algorithm for density estimation in sensor networks. It has been assumed that sensor measurements can be statistically modeled by a common Gaussian mixture model. In the proposed algorithm, mobile agents move through the routes of the network and compute the local sufficient statistics using local measurements. Afterwards, the global sufficient statistics will be updated using these local sufficient statistics. This procedure will be repeated until convergence is reached. Consequently, using this global sufficient statistics the parameters of the density function will be approximated. Convergence of the proposed method will be also analytically studied, and it will be shown that the estimated parameters will eventually converge to their true values. Finally, the proposed algorithm will be applied to one-dimensional and two dimensional data sets to show its promising performance.

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Distributed Sparse Linear Regression

Cited by 465 publications

References 32 publications

Distributed greedy sparse learning over doubly stochastic networks

Distributed greedy sparse learning over doubly stochastic networks

Convergence Rates of Distributed Nesterov-Like Gradient Methods on Random Networks

A Mobile Agent Based Distributed Variational Bayesian Algorithm for Flow and Speed Estimation in a Traffic System

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