Estimating the unknown parameters of a statistical model based on the observations collected by a sensor network is an important problem with application in multiple fields. In this setting, distributed processing, by which computations are carried out within the network in order to avoid raw data transmission to a fusion centre, is a desirable feature resulting in improved robustness and energy savings. In the presence of incomplete data, the expectation-maximisation (EM) algorithm is a popular means to iteratively compute the maximum likelihood (ML) estimate. It has found application in diverse fields such as computational biology, anomaly detection, speech segmentation, reinforcement learning, and motion estimation, among others. In this chapter we will review the formulation of the centralised EM estimation algorithm as a starting point and then discuss distributed versions well suited for implementation in sensor networks. The first class of these distributed versions requires specialised routing through the network in terms of a linear or circular path visiting all nodes, whereas the second class does away with this requirement by using the concept of network consensus to diffuse information through the network. Our focus will be on a relevant sensor network application, in which the parameter of a linear model is to be estimated in the presence of an unknown number of randomly malfunctioning sensors.

%B Data Fusion in Wireless Sensor Networks: A statistical signal processing perspective %I The Institution of Engineering and Technology (IET) %C London, UK %P 201-230 %@ 978-1-78561-584-9 %G eng %& 9 %0 Journal Article %J Signal Processing %D 2018 %T Parameter estimation in wireless sensor networks with faulty transducers: A distributed EM approach %A Silvana Silva Pereira %A R. López-Valcarce %A Alba Pagès-Zamora %K winter %K wsn %XWe address the problem of distributed estimation of a vector-valued parameter performed by a wireless sensor network in the presence of noisy observations which may be unreliable due to faulty transducers. The proposed distributed estimator is based on the Expectation-Maximization (EM) algorithm and combines consensus and diffusion techniques: a term for information diffusion is gradually turned off, while a term for updated information averaging is turned on so that all nodes in the network approach the same value of the estimate. The proposed method requires only local exchanges of information among network nodes and, in contrast with previous approaches, it does not assume knowledge of the a priori probability of transducer failures or the noise variance. A convergence analysis is provided, showing that the convergent points of the centralized EM iteration are locally asymptotically convergent points of the proposed distributed scheme. Numerical examples show that the distributed algorithm asymptotically attains the performance of the centralized EM method.

%B Signal Processing %V 144 %P 226-237 %8 03/2018 %G eng %U https://authors.elsevier.com/a/1W90XbZX4rsob %R 10.1016/j.sigpro.2017.10.012 %0 Conference Paper %B IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP) %D 2017 %T Robust clustering of data collected via crowdsourcing %A Alba Pagès-Zamora %A Georgios Giannakis %A R. López-Valcarce %A Pere Gimenez-Febrer %K winter %K wsn %XCrowdsourcing approaches rely on the collection of multiple individuals to solve problems that require analysis of large data sets in a timely accurate manner. The inexperience of participants or annotators motivates well robust techniques. Focusing on clustering setups, the data provided by all annotators is suitably modeled here as a mixture of Gaussian components plus a uniformly distributed random variable to capture outliers. The proposed algorithm is based on the expectation-maximization algorithm and allows for soft assignments of data to clusters, to rate annotators according to their performance, and to estimate the number of Gaussian components in the non-Gaussian/Gaussian mixture model, in a jointly manner.

%B IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP) %C New Orleans %P 4014 - 4018 %8 03/2017 %G eng %R 10.1109/ICASSP.2017.7952910 %0 Conference Paper %B IEEE Workshop on Statistical Signal Processing (SSP) %D 2016 %T Distributed multivariate regression with unknown noise covariance in the presence of outliers: a minimum description length approach %A R. López-Valcarce %A Daniel Romero %A Josep Sala %A Alba Pagès-Zamora %K compass %K wsn %XWe consider the problem of estimating the coefficients in a multivariable linear model by means of a wireless sensor network

which may be affected by anomalous measurements. The noise covariance matrices at the different sensors are assumed

unknown. Treating outlying samples, and their support, as additional nuisance parameters, the Maximum Likelihood

estimate is investigated, with the number of outliers being estimated according to the Minimum Description Length

principle. A distributed implementation based on iterative consensus techniques is then proposed, and it is shown effective

for managing outliers in the data.

%B IEEE Workshop on Statistical Signal Processing (SSP)
%C Palma de Mallorca, Spain
%G eng
%0 Conference Paper
%B European Signal Processing Conference (EUSIPCO)
%D 2016
%T Online EM-based distributed estimation in sensor networks with faulty nodes
%A Pere Gimenez-Febrer
%A Alba Pagès-Zamora
%A R. López-Valcarce
%K compass
%K wsn
%X This paper focuses on the problem of the distributed estimation of a parameter vector based on noisy observations regularly acquired by the nodes of a wireless sensor network and assuming that some of the nodes have faulty sensors. We propose two online schemes, both centralized and distributed, based on the Expectation-Maximization (EM) algorithm. These algorithms are able to identify and disregard the faulty nodes, and provide a refined estimate of the parameters each time instant after a new set of observations is acquired. Simulation results demonstrate that the centralized versions of the proposed online algorithms attain the same estimation error as the centralized batch EM, whereas the distributed versions come very close to matching the batch EM.

%B European Signal Processing Conference (EUSIPCO)
%C Budapest, Hungary
%8 09/2016
%G eng
%0 Conference Paper
%B IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)
%D 2015
%T Distributed AoA-based Source Positioning in NLOS with Sensor Networks
%A Pere Gimenez-Febrer
%A Alba Pagès-Zamora
%A Silvana Silva Pereira
%A R. López-Valcarce
%K compass
%K wsn
%X This paper focuses on the problem of positioning a source using angle-of-arrival measurements taken by a wireless sensor network in which some of the nodes experience non-line-of-sight (NLOS) propagation conditions. In order to mitigate the errors induced by the nodes in NLOS, we derive an algorithm that combines the expectation-maximization algorithm with a weighted least-squares estimation of the source position so that the nodes in NLOS are eventually identified and discarded. Moreover, a distributed version of this algorithm based on a diffusion strategy that iteratively refines the position estimate while driving the network to a consensus is presented.

%B IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)
%I IEEE
%C Brisbane, Australia
%8 04/2015
%G eng
%0 Conference Paper
%B IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)
%D 2015
%T Distributed TLS Estimation under Random Data Faults
%A Silvana Silva Pereira
%A Alba Pagès-Zamora
%A R. López-Valcarce
%K compass
%K wsn
%X This paper addresses the problem of distributed estimation of a parameter vector in the presence of noisy input and output data as well as data faults, performed by a wireless sensor network in which only local interactions among the nodes are allowed. In the presence of unreliable observations, standard estimators become biased and perform poorly in low signal-to-noise ratios. We propose two different distributed approaches based on the Expectation-Maximization algorithm: in the first one the regressors are estimated at each iteration,

whereas the second one does not require explicit regressor estimation. Numerical results show that the proposed methods approach the performance of a clairvoyant scheme with knowledge of the random data faults.

%B IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)
%I IEEE
%C Brisbane, Australia
%8 04/2015
%G eng
%0 Conference Paper
%B IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)
%D 2014
%T Distributed Total Least Squares Estimation over Networks
%A R. López-Valcarce
%A Silvana Silva Pereira
%A Alba Pagès-Zamora
%K dynacs
%K wsn
%X We consider Total Least Squares (TLS) estimation in a network in which each node has access to a subset of equations of an overdetermined linear system. Previous distributed approaches require that the number of equations at each node be larger than the dimension L of the unknown parameter. We present novel distributed TLS estimators which can handle as few as a single equation per node. In the first scheme, the network computes an extended correlation matrix via standard iterative average consensus techniques, and the TLS estimate is extracted afterwards by means of an eigenvalue decomposition (EVD). The second scheme is EVD-free, but requires that a linear system of size L be solved at each iteration by each node. Replacing this step by a single Gauss-Seidel subiteration is shown to be an effective means to reduce computational cost without sacrificing performance.

%B IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP) %C Florence, Italy %G eng %R 10.1109/ICASSP.2014.6855074 %0 Conference Paper %B IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM) %D 2014 %T How to Implement Doubly-Stochastic Matrices for Consensus-Based Distributed Algorithms %A S. Valcárcel-Macua %A C. Moreno-León %A J. S. Romero %A Silvana Silva Pereira %A Javier Zazo %A Alba Pagès-Zamora %A R. López-Valcarce %A S. Zazo %K compass %K dynacs %K wsn %XDoubly-stochastic matrices are usually required by

consensus-based distributed algorithms. We propose a simple

and efficient protocol and present some guidelines for implementing

doubly-stochastic combination matrices even in noisy,

asynchronous and changing topology scenarios. The proposed

ideas are validated with the deployment of a wireless sensor

network, in which nodes run a distributed algorithm for robust

estimation in the presence of nodes with faulty sensors.

%B IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM)
%C A Coruña, Spain
%G eng
%R 10.1109/SAM.2014.6882409
%0 Conference Paper
%B Int. Conf. Acoust., Speech, Signal Process. (ICASSP)
%D 2013
%T A Diffusion-based distributed EM algorithm for density estimation in wireless sensor networks
%A Silvana Silva Pereira
%A Alba Pagès-Zamora
%A R. López-Valcarce
%K dynacs
%K wsn
%X Distributed implementations of the Expectation-Maximization

(EM) algorithm reported in the literature have been proposed for

applications to solve specific problems. In general, a primary

requirement to derive a distributed solution is that the

structure of the centralized version enables the computation

involving global information in a distributed fashion. This

paper treats the problem of distributed estimation of Gaussian

densities by means of the EM algorithm in wireless sensor

networks using diffusion strategies, where the information

is gradually diffused across the network for the computation

of the global functions. The low-complexity implementation

presented here is based on a two time scale operation

for information averaging and diffusion. The convergence to

a fixed point of the centralized solution has been studied and

the appealing results motivates our choice for this model. Numerical

examples provided show that the performance of the

distributed EM is, in practice, equal to that of the centralized

scheme.

%B Int. Conf. Acoust., Speech, Signal Process. (ICASSP)
%G eng
%R 10.1109/ICASSP.2013.6638501
%0 Journal Article
%J IEEE Signal Processing Letters
%D 2013
%T A Diffusion-Based EM Algorithm for Distributed Estimation in Unreliable Sensor Networks
%A Silvana Silva Pereira
%A R. López-Valcarce
%A Alba Pagès-Zamora
%K dynacs
%K wsn
%X We address the problem of distributed estimation of a parameter from a set of noisy observations collected by a sensor network, assuming that some sensors may be subject to data failures and report only noise. In such scenario, simple schemes such as the Best Linear Unbiased Estimator result in an error floor in moderate and high signal-to-noise ratio (SNR), whereas previously proposed methods based on hard decisions on data failure events degrade as the SNR decreases. Aiming at optimal performance within the whole range of SNRs, we adopt a Maximum Likelihood framework based on the Expectation-Maximization (EM) algorithm. The statistical model and the iterative nature of the EM method allow for a diffusion-based distributed implementation, whereby the information propagation is embedded in the iterative update of the parameters. Numerical examples show that the proposed algorithm practically attains the Cramer–Rao Lower Bound at all SNR values and compares favorably with other approaches.

%B IEEE Signal Processing Letters %V 20 %P 595-598 %8 06/2013 %G eng %N 6 %& 595 %R 10.1109/LSP.2013.2260329