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Many real time series datasets exhibit structural changes over time. A popular model for capturing their temporal dependence is that of vector autoregressions (VAR), which can accommodate structural changes through time evolving transition matrices. The problem then becomes to both estimate the (unknown) number of structural break points, together with the VAR model parameters. An additional challenge emerges in the presence of very large datasets, namely on how to accomplish these two objectives in a computational efficient manner. In this article, we propose a novel procedure which leverages a block segmentation scheme (BSS) that reduces the number of model parameters to be estimated through a regularized least-square criterion. Specifically, BSS examines appropriately defined blocks of the available data, which when combined with a fused lasso-based estimation criterion, leads to significant computational gains without compromising on the statistical accuracy in identifying the number and location of the structural breaks. This procedure is further coupled with new local and exhaustive search steps to consistently estimate the number and relative location of the break points. The procedure is scalable to big high-dimensional time series datasets with a computational complexity that can achieve O(n), where n is the length of the time series (sample size), compared to an exhaustive procedure that requires steps. Extensive numerical work on synthetic data supports the theoretical findings and illustrates the attractive properties of the procedure. Finally, an application to a neuroscience dataset exhibits its usefulness in applications. Supplementary files for this article are available online. 

High dimensional piecewise stationary graphical models represent a versatile class for modelling time varying networks arising in diverse application areas, including biology, economics, and social sciences. There has been recent work in offline detection and estimation of regime changes in the topology of sparse graphical models. However, the online setting remains largely unexplored, despite its high relevance to applications in sensor networks and other engineering monitoring systems, as well as financial markets. To that end, this work introduces a novel scalable online algorithm for detecting an unknown number of abrupt changes in the inverse covariance matrix of sparse Gaussian graphical models with small delay. The proposed algorithm is based upon monitoring the conditional log-likelihood of all nodes in the network and can be extended to a large class of continuous and discrete graphical models. We also investigate asymptotic properties of our procedure under certain mild regularity conditions on the graph size, sparsity level, number of samples, and pre- and post-changes in the topology of the network. Numerical works on both synthetic and real data illustrate the good performance of the proposed methodology both in terms of computational and statistical efficiency across numerous experimental settings. 

We consider the problem of estimating the location of a single change point in a network generated by a dynamic stochastic block model mechanism. This model produces community structure in the network that exhibits change at a single time epoch. We propose two methods of estimating the change point, together with the model parameters, before and after its occurrence. The first employs a least-squares criterion function and takes into consideration the full structure of the stochastic block model and is evaluated at each point in time. Hence, as an intermediate step, it requires estimating the community structure based on a clustering algorithm at every time point. The second method comprises the following two steps: in the first one, a least-squares function is used and evaluated at each time point, but ignoring the community structure and only considering a random graph generating mechanism exhibiting a change point. Once the change point is identified, in the second step, all network data before and after it are used together with a clustering algorithm to obtain the corresponding community structures and subsequently estimate the generating stochastic block model parameters. The first method, since it requires knowledge of the community structure and hence clustering at every point in time, is significantly more computationally expensive than the second one. On the other hand, it requires a significantly less stringent identifiability condition for consistent estimation of the change point and the model parameters than the second method; however, it also requires a condition on the misclassification rate of misallocating network nodes to their respective communities that may fail to hold in many realistic settings. Despite the apparent stringency of the identifiability condition for the second method, we show that networks generated by a stochastic block mechanism exhibiting a change in their structure can easily satisfy this condition under a multitude of scenarios, including merging/splitting communities, nodes joining another community, etc. Further, for both methods under their respective identifiability and certain additional regularity conditions, we establish rates of convergence and derive the asymptotic distributions of the change point estimators. The results are illustrated on synthetic data. In summary, this work provides an in-depth investigation of the novel problem of change point analysis for networks generated by stochastic block models, identifies key conditions for the consistent estimation of the change point, and proposes a computationally fast algorithm that solves the problem in many settings that occur in applications. Finally, it discusses challenges posed by employing clustering algorithms in this problem, that require additional investigation for their full resolution. 

The bi-directional communication capabilities that emerged into the smart power grid play a critical role in the grid's secure, reliable and efficient operation. Nevertheless, the data communication functionalities introduced to Advanced Metering Infrastructure (AMI) nodes end the grid's isolation, and expose the network into an array of cyber-security threats that jeopardize the grid's stability and availability. For instance, malware amenable to inject false data into the AMI can compromise the grid's state estimation process and lead to catastrophic power outages. In this paper, we explore several statistical spatio-temporal models for efficient diagnosis of false data injection attacks in smart grids. The proposed methods leverage the data co-linearities that naturally arise in the AMI measurements of the electric network to provide forecasts for the network's AMI observations, aiming to quickly detect the presence of “bad data”. We evaluate the proposed approaches with data tampered with stealth attacks compiled via three different attack strategies. Further, we juxtapose them against two other forecasting-aided detection methods appearing in the literature, and discuss the trade-offs of all techniques when employed on real-world power grid data, obtained from a large university campus.