Theoretical Bounds on MAP Estimation in Distributed Sensing Networks

05/30/2018
by   Ali Bereyhi, et al.
0

The typical approach for recovery of spatially correlated signals is regularized least squares with a coupled regularization term. In the Bayesian framework, this algorithm is seen as a maximum-a-posterior estimator whose postulated prior is proportional to the regularization term. In this paper, we study distributed sensing networks in which a set of spatially correlated signals are measured individually at separate terminals, but recovered jointly via a generic maximum-a-posterior estimator. Using the replica method, it is shown that the setting exhibits the decoupling property. For the case with jointly sparse signals, we invoke Bayesian inference and propose the "multi-dimensional soft thresholding" algorithm which is posed as a linear programming. Our investigations depict that the proposed algorithm outperforms the conventional ℓ_2,1-norm regularized least squares scheme while enjoying a feasible computational complexity.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/25/2016

Communication-Efficient Distributed Statistical Inference

We present a Communication-efficient Surrogate Likelihood (CSL) framewor...
research
07/07/2016

Kernel Bayesian Inference with Posterior Regularization

We propose a vector-valued regression problem whose solution is equivale...
research
08/11/2016

Distributed learning with regularized least squares

We study distributed learning with the least squares regularization sche...
research
03/14/2012

A Proximal-Gradient Homotopy Method for the Sparse Least-Squares Problem

We consider solving the ℓ_1-regularized least-squares (ℓ_1-LS) problem i...
research
02/12/2014

Sparse Estimation From Noisy Observations of an Overdetermined Linear System

This note studies a method for the efficient estimation of a finite numb...
research
07/28/2018

Holographic Sensing

Holographic representations of data encode information in packets of equ...
research
05/30/2018

RLS Recovery with Asymmetric Penalty: Fundamental Limits and Algorithmic Approaches

This paper studies regularized least square recovery of signals whose sa...

Please sign up or login with your details

Forgot password? Click here to reset