### Dynamic Structural Equation Models for Tracking Cascades Over Social Networks

"... Many real-world processes evolve in cascades over networks, whose topologies are often unobservable and change over time. However, the so-termed adoption times when for instance blogs mention popular news items are typically known, and are implicitly dependent on the underlying network. To infer the ..."

Abstract
- Add to MetaCart

(Show Context)
Many real-world processes evolve in cascades over networks, whose topologies are often unobservable and change over time. However, the so-termed adoption times when for instance blogs mention popular news items are typically known, and are implicitly dependent on the underlying network. To infer the network topology, a dynamic structural equation model is adopted to capture the relationship between observed adoption times and the unknown edge weights. Assuming a slowly time-varying topology and leveraging the sparse connectivity inherent to social networks, edge weights are estimated by minimizing a sparsity-regularized exponentially-weighted least-squares criterion. To this end, a solver is developed by leveraging (pseudo) real-time sparsity-promoting proximal gradient iterations. Numerical tests with synthetic data and real cascades of online media demonstrate the effectiveness of the novel algorithm in unveiling sparse dynamically-evolving topologies, while accounting for external influences in the adoption times. 1

### Channel Gain Cartography via Low Rank and Sparsity

"... Abstract—Channel gain cartography aims at inferring the channel gains between arbitrary points in space based on mea-surements (samples) of channel gains taken from finite pairs of transceivers. Channel gain maps are useful for various sensing and resource allocation tasks, essential for the operati ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract—Channel gain cartography aims at inferring the channel gains between arbitrary points in space based on mea-surements (samples) of channel gains taken from finite pairs of transceivers. Channel gain maps are useful for various sensing and resource allocation tasks, essential for the operation of cognitive radio networks. In this work, the channel gain samples are modeled as compressive tomographic measurements of an underlying spatial loss field (SLF), postulated to have low-rank structure corrupted by sparse errors. Efficient algorithms to reconstruct the SLF are developed, from which arbitrary channel gains can be interpolated. I.

### ROBUST NETWORK TRAFFIC ESTIMATION VIA SPARSITY AND LOW RANK

"... Accurate estimation of origin-to-destination (OD) traffic flows pro-vides valuable input for network management tasks. However, lack of flow-level observations as well as intentional and unintentional anomalies pose major challenges toward achieving this goal. Lever-aging the low intrinsic-dimension ..."

Abstract
- Add to MetaCart

(Show Context)
Accurate estimation of origin-to-destination (OD) traffic flows pro-vides valuable input for network management tasks. However, lack of flow-level observations as well as intentional and unintentional anomalies pose major challenges toward achieving this goal. Lever-aging the low intrinsic-dimensionality of OD flows and the sparse nature of anomalies, this paper proposes a convex program with nuclear-norm and ℓ1-norm regularization terms to estimate the nom-inal and anomalous traffic components, using a small subset of (pos-sibly anomalous) flow counts in addition to link counts. Analysis and simulations confirm that the said estimator can exactly recover suf-ficiently low-dimensional nominal traffic and sparse enough anoma-lies when the routing matrix is column-incoherent, and an adequate amount of flow counts are randomly sampled. The results offer valu-able insights about the measurement types and network scenaria giv-ing rise to accurate traffic estimation. Tests with real Internet data corroborate the effectiveness of the novel estimator. Index Terms — Sparsity, low rank, traffic estimation. 1.

### Decentralized Learning for Wireless Communications and Networking

"... Abstract This chapter deals with decentralized learning algorithms for in-network processing of graph-valued data. A generic learning problem is formulated and re-cast into a separable form, which is iteratively minimized using the alternating-direction method of multipliers (ADMM) so as to gain the ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract This chapter deals with decentralized learning algorithms for in-network processing of graph-valued data. A generic learning problem is formulated and re-cast into a separable form, which is iteratively minimized using the alternating-direction method of multipliers (ADMM) so as to gain the desired degree of paral-lelization. Without exchanging elements from the distributed training sets and keep-ing inter-node communications at affordable levels, the local (per-node) learners consent to the desired quantity inferred globally, meaning the one obtained if the entire training data set were centrally available. Impact of the decentralized learn-ing framework to contemporary wireless communications and networking tasks is illustrated through case studies including target tracking using wireless sensor net-works, unveiling Internet traffic anomalies, power system state estimation, as well as spectrum cartography for wireless cognitive radio networks.

### Proximal-Gradient Algorithms for Tracking Cascades Over Social Networks

"... Abstract—Many real-world processes evolve in cascades over complex networks, whose topologies are often unobservable and change over time. However, the so-termed adoption times when blogs mention popular news items, individuals in a community catch an infectious disease, or consumers adopt a trendy ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract—Many real-world processes evolve in cascades over complex networks, whose topologies are often unobservable and change over time. However, the so-termed adoption times when blogs mention popular news items, individuals in a community catch an infectious disease, or consumers adopt a trendy elec-tronics product are typically known, and are implicitly dependent on the underlying network. To infer the network topology, a dynamic structural equation model is adopted to capture the rela-tionship between observed adoption times and the unknown edge weights. Assuming a slowly time-varying topology and leveraging the sparse connectivity inherent to social networks, edge weights are estimated by minimizing a sparsity-regularized exponen-tially-weighted least-squares criterion. To this end, solvers with complementary strengths are developed by leveraging (pseudo) real-time sparsity-promoting proximal gradient iterations, the improved convergence rate of accelerated variants, or reduced computational complexity of stochastic gradient descent. Nu-merical tests with both synthetic and real data demonstrate the effectiveness of the novel algorithms in unveiling sparse dynami-cally-evolving topologies, while accounting for external influences in the adoption times. Key events in the political leadership in North Korea and the initial public offering of LinkedIn explain connectivity changes observed in the associated networks inferred from global cascades of online media. Index Terms—Structural equation model, dynamic network, so-cial network, contagion, sparsity. I.

### Imputation of Streaming Low-Rank Tensor Data

"... Abstract—Unraveling latent structure by means of multilinear models of tensor data is of paramount importance in timely inference tasks encountered with ‘Big Data ’ analytics. However, increasingly noisy, heterogeneous, and incomplete datasets as well as the need for real-time processing of streamin ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract—Unraveling latent structure by means of multilinear models of tensor data is of paramount importance in timely inference tasks encountered with ‘Big Data ’ analytics. However, increasingly noisy, heterogeneous, and incomplete datasets as well as the need for real-time processing of streaming data pose major challenges to this end. The present paper introduces a novel online (adaptive) algorithm to decompose low-rank tensors with missing entries, and perform imputation as a byproduct. The nov-el estimator minimizes an exponentially-weighted least-squares fitting error along with a separable regularizer of the PARAFAC decomposition factors, to trade-off fidelity for complexity of the approximation captured by the decomposition’s rank. Leverag-ing stochastic gradient descent iterations, a scalable, real-time algorithm is developed and its convergence is established under simplifying technical assumptions. Simulated tests with cardiac magnetic resonance imagery (MRI) data confirm the efficacy of the proposed algorithm in imputing up to 75 % missing entries. I.

### 1A Correctness Result for Online Robust PCA Brian Lois, Graduate Student Member, IEEE

"... This work studies the problem of sequentially recovering a sparse vector xt and a vector from a low-dimensional subspace `t from knowledge of their sum mt = xt + `t. If the primary goal is to recover the low-dimensional subspace where the `t’s lie, then the problem is one of online or recursive robu ..."

Abstract
- Add to MetaCart

(Show Context)
This work studies the problem of sequentially recovering a sparse vector xt and a vector from a low-dimensional subspace `t from knowledge of their sum mt = xt + `t. If the primary goal is to recover the low-dimensional subspace where the `t’s lie, then the problem is one of online or recursive robust principal components analysis (PCA). To the best of our knowledge, this is the first correctness result for online robust PCA. We prove that if the `t’s obey certain denseness and slow subspace change assumptions, and the support of xt changes by at least a certain amount at least every so often, and some other mild assumptions hold, then with high probability, the support of xt will be recovered exactly, and the error made in estimating xt and `t will be small. An example of where such a problem might arise is in separating a sparse foreground and slowly changing dense background in a surveillance video. I.