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Abstract Learning the topology of a graph from available data is of great interest in many emerging applications. Some examples are social networks, internet of things networks (intelligent IoT and industrial IoT), biological connection networks, sensor networks and traffic network patterns. In this paper, a graph topology inference approach is proposed to learn the underlying graph structure from a given set of noisy multi-variate observations, which are modeled as graph signals generated from a Gaussian Markov Random Field (GMRF) process. A factor analysis model is applied to represent the graph signals in a latent space where the basis is related to the underlying graph structure. An optimal graph filter is also developed to recover the graph signals from noisy observations. In the final step, an optimization problem is proposed to learn the underlying graph topology from the recovered signals. Moreover, a fast algorithm employing the proximal point method has been proposed to solve the problem efficiently. Experimental results employing both synthetic and real data show the effectiveness of the proposed method in recovering the signals and inferring the underlying graph.

A quickest change detection problem is considered in a sensor network with observations whose statistical dependency structure across the sensors before and after the change is described by a decomposable graphical model (DGM). Distributed computation methods for this problem are proposed that are capable of producing the optimum centralized test statistic. The DGM leads to the proper way to collect nodes into local groups equivalent to cliques in the graph, such that a clique statistic which summarizes all the clique sensor data can be computed within each clique. The clique statistics are transmitted to a decision maker to produce the optimum centralized test statistic. In order to further improve communication efficiency, an ordered transmission approach is proposed where transmissions of the clique statistics to the fusion center are ordered and then adaptively halted when sufficient information is accumulated. This procedure is always guaranteed to provide the optimal change detection performance, despite not transmitting all the statistics from all the cliques. A lower bound on the average number of transmissions saved by ordered transmissions is provided and for the case where the change seldom occurs the lower bound approaches approximately half the number of cliques provided a well behaved distance measuremore »between the distributions of the sensor observations before and after the change is sufficiently large. We also extend the approach to the case when the graph structure is different under each hypothesis. Numerical results show significant savings using the ordered transmission approach and validate the theoretical findings.« less

Quickest change detection in a sensor network is considered where each sensor observes a sequence of random variables and transmits its local information on the observations to a fusion center. At an unknown point in time, the distribution of the observations at all sensors changes. The objective is to detect the change in distribution as soon as possible, subject to a false alarm constraint. We consider minimax formulations for this problem and propose a new approach where transmissions are ordered and halted when sufficient information is accumulated at the fusion center. We show that the proposed approach can achieve the optimal performance equivalent to the centralized cumulative sum (CUSUM) algorithm while requiring fewer sensor transmissions. Numerical results for a shift in mean of independent and identically distributed Gaussian observations show significant communication savings for the case where the change seldom occurs which is frequently true in many important applications.

The topic of training machine learning models by employing multiple gradient-computing workers is attracting great interest recently. Communication efficiency in such distributed learning settings is an important consideration, especially for the case where the needed communications are expensive in terms of power usage. We develop a new approach which is efficient in terms of communication transmissions. In this scheme, only the most informative worker results are transmitted to reduce the total number of transmissions. Our ordered gradient approach provably achieves the same order of convergence rate as gradient descent for nonconvex smooth loss functions while gradient descent always requires more communications. Experiments show significant communication savings compared to the best existing approaches in some cases.

In this paper, we develop efficient methods for devising lower complexity receivers that can achieve performance close to the full complexity receivers for passive/active multiple-input multiple-output (MIMO) radar. The method employed eliminates some parts of the test statistic to lower either hardware or software complexity. For the case of spatially uncorrelated reflection coefficients and spatially white clutter-plus-noise, the test statistic requires the computation of a set of matched filters, each matched to a signal from a different transmitter. In this case, our method is equivalent to selecting a specific set of transmitters to provide optimum performance. In the more general case of correlated clutter-plus-noise and reflection coefficients, then the test statistic requires the computation of a larger set of matched filters. These matched filters correlate the clutter-plus-noise free signal received at one receive antenna due to the signal transmitted from some transmit antenna and the signal received at another receive antenna. In the more general case, our algorithm picks the best of these matched filters to implement when the total number of these matched filters one can implement is limited.

The estimation of a meaningful affinity graph has become a crucial task for representation of data, since the underlying structure is not readily available in many applications. In this paper, a topology inference framework, called Bayesian Topology Learning, is proposed to estimate the underlying graphtopologyfromagivensetofnoisymeasurementsofsignals. It is assumed that the graph signals are generated from GaussianMarkovRandomFieldprocesses. First,usingafactor analysis model, the noisy measured data is represented in a latent space and its posterior probability density function is found. Thereafter, by utilizing the minimum mean square error estimator and the Expectation Maximization (EM) procedure, a filter is proposed to recover the signal from noisy measurements and an optimization problem is formulated to estimatetheunderlyinggraphtopology. Theexperimentalresults show that the proposed method has better performance whencomparedtothecurrentstate-of-the-artalgorithmswith different performance measures.