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Recovering a graph signal from samples is a central problem in graph signal processing. Least mean squares (LMS) method for graph signal estimation is computationally efficient adaptive method. In this paper, we introduce a technique to robustify LMS with respect to mismatches in the presumed graph topology. It builds on the fact that graph LMS converges faster when the graph topology is specified correctly. We consider two measures of convergence speed, based on which we develop randomized greedy algorithms for robust interpolation of graph signals.

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Community detection from graphs has many applications
in machine learning, biological and social sciences. While
there is a broad spectrum of literature based on various
approaches, recently there has been a significant focus on
inference algorithms for statistical models of community
structure. These algorithms strive to solve an inference
problem based on a generative model of the network. Recent
advances in stochastic gradient MCMC have played a crucial
role in improving the scalability of these techniques. In this

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Distributed estimation of a parameter vector in a network of sensor nodes with ambiguous measurements is considered. The ambiguities are modelled by following a set-theoretic approach, that leads to each sensor employing a non-convex constraint set on the parameter vector. Consensus can be used to reach an estimate consistent with the measurements of all nodes, assuming that such an estimate exists, but unfortunately, such an approach leads to a non-convex problem.

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In this work we present novel provably accelerated gossip algorithms for solving the average consensus problem. The proposed protocols are inspired from the recently developed accelerated variants of the randomized Kaczmarz method - a popular method for solving linear systems. In each gossip iteration all nodes of the network update their values but only a pair of them exchange their private information. Numerical experiments on popular wireless sensor networks showing the benefits of our protocols are also presented.

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In this paper, we present an efficient method for radio frequency interference (RFI) detection based on cyclic spectrum analysis that relies on compressive statistical sensing to estimate the cyclic spectrum from sub-Nyquist data. We refer to this method as compressive statistical sensing (CSS), since we utilize the statistical autocovariance matrix from the compressed data.

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In this paper, we discuss the problem of modeling a graph signal on a directed graph when observing only partially the graph signal. The graph signal is recovered using a learned graph filter. The novelty is to use the random walk operator associated to an ergodic random walk on the graph, so as to define and learn a graph filter, expressed as a polynomial of this operator. Through the study of different cases, we show the efficiency of the signal modeling using the random walk operator compared to existing methods using the adjacency matrix or ignoring the directions in the graph.

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