The Lasso is a popular technique for joint estimation and continuous variable selection, especially well-suited for sparse and possibly under-determined linear regression problems. This paper develops algorithms to estimate the regression coefficients via Lasso when the training data are distributed across different agents, and their communication to a central processing unit is prohibited for e.g., communication cost or privacy reasons. A motivating application is explored in the context of wireless communications, whereby sensing cognitive radios collaborate to estimate the radio-frequency power spectrum density. Attaining different tradeoffs between complexity and convergence speed, three novel algorithms are obtained after reformulating the Lasso into a separable form, which is iteratively minimized using the alternating-direction method of multipliers so as to gain the desired degree of parallelization. Interestingly, the per agent estimate updates are given by simple soft-thresholding operations, and inter-agent communication overhead remains at affordable level. Without exchanging elements from the different training sets, the local estimates consent to the global Lasso solution, i.e., the fit that would be obtained if the entire data set were centrally available. Numerical experiments with both simulated and real data demonstrate the merits of the proposed distributed schemes, corroborating their convergence and global optimality. The ideas in this paper can be easily extended for the purpose of fitting related models in a distributed fashion, including the adaptive Lasso, elastic net, fused Lasso and nonnegative garrote.

Among the panoply of applications enabled by the Internet of Things (IoT), smart and connected health care is a particularly important one. Networked sensors, either worn on the body or embedded in our living environments, make possible the gathering of rich information indicative of our physical and mental health. Captured on a continual basis, aggregated, and effectively mined, such information can bring about a positive transformative change in the health care landscape. In particular, the availability of data at hitherto unimagined scales and temporal longitudes coupled with a new generation of intelligent processing algorithms can: (a) facilitate an evolution in the practice of medicine, from the current post facto diagnose-and-treat reactive paradigm, to a proactive framework for prognosis of diseases at an incipient stage, coupled with prevention, cure, and overall management of health instead of disease, (b) enable personalization of treatment and management options targeted particularly to the specific circumstances and needs of the individual, and (c) help reduce the cost of health care while simultaneously improving outcomes. In this paper, we highlight the opportunities and challenges for IoT in realizing this vision of the future of health care.

Network topology inference is a significant problem in network science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known and then analyze how the graph?s algebraic and spectral characteristics impact the properties of the graph signals of interest. Such an assumption is often untenable beyond applications dealing with, e.g., directly observable social and infrastructure networks; and typically adopted graph construction schemes are largely informal, distinctly lacking an element of validation. This article offers an overview of graph-learning methods developed to bridge the aforementioned gap, by using information available from graph signals to infer the underlying graph topology. Fairly mature statistical approaches are surveyed first, where correlation analysis takes center stage along with its connections to covariance selection and high-dimensional regression for learning Gaussian graphical models. Recent GSP-based network inference frameworks are also described, which postulate that the network exists as a latent underlying structure and that observations are generated as a result of a network process defined in such a graph. A number of arguably more nascent topics are also briefly outlined, including inference of dynamic networks and nonlinear models of pairwise interaction, as well as extensions to directed (di) graphs and their relation to causal inference. All in all, this article introduces readers to challenges and opportunities for SP research in emerging topic areas at the crossroads of modeling, prediction, and control of complex behavior arising in networked systems that evolve over time.

Adaptive algorithms based on in-network processing of distributed observations are well-motivated for online parameter estimation and tracking of (non)stationary signals using ad hoc wireless sensor networks (WSNs). To this end, a fully distributed least mean-square (D-LMS) algorithm is developed in this paper, offering simplicity and flexibility while solely requiring single-hop communications among sensors. The resultant estimator minimizes a pertinent squared-error cost by resorting to i) the alternating-direction method of multipliers so as to gain the desired degree of parallelization and ii) a stochastic approximation iteration to cope with the time-varying statistics of the process under consideration. Information is efficiently percolated across the WSN using a subset of ldquobridgerdquo sensors, which further tradeoff communication cost for robustness to sensor failures. For a linear data model and under mild assumptions aligned with those considered in the centralized LMS, stability of the novel D-LMS algorithm is established to guarantee that local sensor estimation error norms remain bounded most of the time. Interestingly, this weak stochastic stability result extends to the pragmatic setup where intersensor communications are corrupted by additive noise. In the absence of observation and communication noise, consensus is achieved almost surely as local estimates are shown exponentially convergent to the parameter of interest with probability one. Mean-square error performance of D-LMS is also assessed. Numerical simulations: i) illustrate that D-LMS outperforms existing alternatives that rely either on information diffusion among neighboring sensors, or, local sensor filtering; ii) highlight its tracking capabilities; and iii) corroborate the stability and performance analysis results.

We address the problem of identifying the structure of an undirected graph from the observation of signals defined on its nodes. Fundamentally, the unknown graph encodes direct relationships between signal elements, which we aim to recover from observable indirect relationships generated by a diffusion process on the graph. The fresh look advocated here leverages concepts from convex optimization and stationarity of graph signals, in order to identify the graph shift operator (a matrix representation of the graph) given only its eigenvectors. These spectral templates can be obtained, e.g., from the sample covariance of independent graph signals diffused on the sought network. The novel idea is to find a graph shift that, while being consistent with the provided spectral information, endows the network with certain desired properties such as sparsity. To that end, we develop efficient inference algorithms stemming from provably tight convex relaxations of natural nonconvex criteria, particularizing the results for two shifts: the adjacency matrix and the normalized Laplacian. Algorithms and theoretical recovery conditions are developed not only when the templates are perfectly known, but also when the eigenvectors are noisy or when only a subset of them are given. Numerical tests showcase the effectiveness of the proposed algorithms in recovering synthetic and real-world networks.

With pervasive sensors continuously collecting and storing massive amounts of information, there is no doubt this is an era of data deluge. Learning from these large volumes of data is expected to bring significant science and engineering advances along with improvements in quality of life. However, with such a big blessing come big challenges. Running analytics on voluminous data sets by central processors and storage units seems infeasible, and with the advent of streaming data sources, learning must often be performed in real time, typically without a chance to revisit past entries. Workhorse signal processing (SP) and statistical learning tools have to be re-examined in todays high-dimensional data regimes. This article contributes to the ongoing cross-disciplinary efforts in data science by putting forth encompassing models capturing a wide range of SP-relevant data analytic tasks, such as principal component analysis (PCA), dictionary learning (DL), compressive sampling (CS), and subspace clustering. It offers scalable architectures and optimization algorithms for decentralized and online learning problems, while revealing fundamental insights into the various analytic and implementation tradeoffs involved. Extensions of the encompassing models to timely data-sketching, tensor- and kernel-based learning tasks are also provided. Finally, the close connections of the presented framework with several big data tasks, such as network visualization, decentralized and dynamic estimation, prediction, and imputation of network link load traffic, as well as imputation in tensor-based medical imaging are highlighted.