@inbook {956, title = {Expectation{\textendash}maximisation based distributed estimation in sensor networks}, booktitle = {Data Fusion in Wireless Sensor Networks: A statistical signal processing perspective}, year = {2019}, pages = {201-230}, publisher = {The Institution of Engineering and Technology (IET)}, organization = {The Institution of Engineering and Technology (IET)}, chapter = {9}, address = {London, UK}, abstract = {
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.
}, keywords = {winter, wsn}, isbn = {978-1-78561-584-9}, author = {R. L{\'o}pez-Valcarce and Alba Pag{\`e}s-Zamora} } @article {913, title = {Parameter estimation in wireless sensor networks with faulty transducers: A distributed EM approach}, journal = {Signal Processing}, volume = {144}, year = {2018}, month = {03/2018}, pages = {226-237}, abstract = {We 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.
}, keywords = {winter, wsn}, doi = {10.1016/j.sigpro.2017.10.012}, url = {https://authors.elsevier.com/a/1W90XbZX4rsob}, author = {Silvana Silva Pereira and R. L{\'o}pez-Valcarce and Alba Pag{\`e}s-Zamora} } @conference {876, title = {Robust clustering of data collected via crowdsourcing}, booktitle = {IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)}, year = {2017}, month = {03/2017}, pages = {4014 - 4018}, address = {New Orleans}, abstract = {Crowdsourcing 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.
}, keywords = {winter, wsn}, doi = {10.1109/ICASSP.2017.7952910}, author = {Alba Pag{\`e}s-Zamora and Georgios Giannakis and R. L{\'o}pez-Valcarce and Pere Gimenez-Febrer} } @conference {845, title = {Distributed multivariate regression with unknown noise covariance in the presence of outliers: a minimum description length approach}, booktitle = {IEEE Workshop on Statistical Signal Processing (SSP)}, year = {2016}, address = {Palma de Mallorca, Spain}, abstract = {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.
}, keywords = {dynacs, wsn}, doi = {10.1109/ICASSP.2014.6855074}, author = {R. L{\'o}pez-Valcarce and Silvana Silva Pereira and Alba Pag{\`e}s-Zamora} } @conference {733, title = {How to Implement Doubly-Stochastic Matrices for Consensus-Based Distributed Algorithms}, booktitle = {IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM)}, year = {2014}, address = {A Coru{\~n}a, Spain}, abstract = {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{\textendash}Rao Lower Bound at all SNR values and compares favorably with other approaches.
}, keywords = {dynacs, wsn}, doi = {10.1109/LSP.2013.2260329}, author = {Silvana Silva Pereira and R. L{\'o}pez-Valcarce and Alba Pag{\`e}s-Zamora} }