Estimation of Space-Time Varying Parameters Using a Diffusion LMS Algorithm

Self Cite

We consider distributed multitask learning problems over a network of agents where each agent is interested in estimating its own parameter vector, also called task, and where the tasks at neighboring agents are related according to a set of linear equality constraints. Each agent possesses its own convex cost function of its parameter vector and a set of linear equality constraints involving its own parameter vector and the parameter vectors of its neighboring agents. We propose an adaptive stochastic algorithm based on the projection gradient method and diffusion strategies in order to allow the network to optimize the individual costs subject to all constraints. Although the derivation is carried out for linear equality constraints, the technique can be applied to other forms of convex constraints. We conduct a detailed mean-square-error analysis of the proposed algorithm and derive closed-form expressions to predict its learning behavior. We provide simulations to illustrate the theoretical findings. Finally, the algorithm is employed for solving two problems in a distributed manner: a minimum-cost flow problem over a network and a space-time varying field reconstruction problem.subject to ∈Ip D p w + b p = 0, p = 1, . . . , P. (1b) Each agent k in the network seeks to estimate its own M k × 1 parameter vector w k , and has knowledge of its cost function J k (·) and the set of linear equality constraints that agent k is involved in. Each constraint is indexed by p, and defined by the L p × M matrices D p , the L p × 1 vector b p , and the set

Section: A Network Error Vector Recursionmentioning

confidence: 99%

Diffusion LMS for Multitask Problems With Local Linear Equality Constraints

Nassif

Richard

Ferrari

et al. 2017

Self Cite

“…Instead of recursively trying to minimize a cost function, the goal, in this case, is to find a set of solutions that are in agreement with the available measurements and the sparsity constraints. For example, the work of [102] develops an algorithm that finds all vectors h that belong to the intersection of the sets S j Other work on the topic includes [104] (Kalman filter based sparse adaptive filter), [105] ("proportionate-type algorithms" for online sparsity-aware system identification problems), [106] (combine sparsity-promoting schemes with dataselection mechanisms), [107] (greedy sparse RLS), [108] (recursive ℓ 1,∞ group LASSO), [109] (variational Bayes framework for sparse adaptive filtering) and [110], [111] (distributed adaptive filtering).…”

Section: B Sparsity-aware Adaptive Filtering and Its Application To mentioning

confidence: 99%

Recursive Recovery of Sparse Signal Sequences From Compressive Measurements: A Review

Vaswani

Zhan

2016

Abstract-In this article, we review the literature on design and analysis of recursive algorithms for reconstructing a time sequence of sparse signals from compressive measurements. The signals are assumed to be sparse in some transform domain or in some dictionary. Their sparsity patterns can change with time, although, in many practical applications, the changes are gradual. An important class of applications where this problem occurs is dynamic projection imaging, e.g., dynamic magnetic resonance imaging (MRI) for real-time medical applications such as interventional radiology, or dynamic computed tomography.

“…For instance, sensor networks deployed to estimate a spatiallyvarying temperature profile need to exploit more directly the spatio-temporal correlations that exist between measurements at neighboring nodes [21]. Likewise, monitoring applications where agents need to track the movement of multiple correlated targets need to exploit the correlation profile in the data for enhanced accuracy.…”

Section: Introductionmentioning

confidence: 99%

Multitask Diffusion Adaptation OverAsynchronous Networks

Nassif

Richard

Ferrari

et al. 2016

Self Cite

Abstract-The multitask diffusion LMS is an efficient strategy to simultaneously infer, in a collaborative manner, multiple parameter vectors. Existing works on multitask problems assume that all agents respond to data synchronously. In several applications, agents may not be able to act synchronously because networks can be subject to several sources of uncertainties such as changing topology, random link failures, or agents turning on and off for energy conservation. In this work, we describe a model for the solution of multitask problems over asynchronous networks and carry out a detailed mean and mean-square error analysis. Results show that sufficiently small step-sizes can still ensure both stability and performance. Simulations and illustrative examples are provided to verify the theoretical findings.