Operational and safety goals for the built environment demand robust, scalable and reliable large scale monitoring for infrastructure systems. High performance real-time event detection and decision making requires models and algorithms to process large amounts of data from dense sensor networks deployed in these systems. Despite advances in the development of detection algorithms for such networks, there are two widely recognized and conflicting obstacles: detection rules need to be sufficiently complex to adapt to the spatiotemporal changes in the environment, requiring the sharing of data; but rules are constrained by statistical performance guarantees and computation and communications budgets imposed by the network. This project addresses these challenges by developing a fundamentally new approach that jointly accounts for statistical detection, communication constraints and distributed computation. This research develops a framework that integrates the distributed computation and communication constraints of the underlying network infrastructure with flexible stochastic modeling and learning algorithms with spatiotemporal data. The modeling and algorithms enable simultaneous and sequential decision making at many local sites, by borrowing information across the network in a statistically coherent and computationally efficient manner. Combining the formalism of sequential change point detection, nonparametric and probabilistic graphical models and spatiotemporal statistics, the project develops distributed and sequential message-passing algorithms for detecting changes in the underlying distributions generating network data. The models developed also offer new theoretical understanding of the trade-offs between statistical model complexity, distributed computation efficiency, and structure of communication constraints within the network.
This interdisciplinary research brings together students and researchers from different areas, utilizing and developing knowledge and cross-disciplinary skills in the fields of computer science, statistics, signal processing and civil engineering.
Distributed detection and decision-making in large-scale sensor networks for infrastructure monitoring is an important problem that lies at the intersections of signal processing, computer science and engineering fields. To increase the applicability and effectiveness of such powerful technologies in an array of data-driven settings, new methods are developed to address the complexity of the spatiotemporal environmental patterns, in addition to the physical and computational constrains imposed by the distributed data sources and data collection devices. This main theme of this project was to draw on ideas and integrate techniques from the separate fields of statistics, signal processing and computation, so as to synthesize new solutions that address such modeling and algorithmic challenges in distributed detection and decision making. Intellectual achievements This project has made a number of contributions, which are organized in a number of dimensions. In terms of problems, we have successfully formulated and solved several challenging detection problems, including multiple change point detection in a network setting, using the graphical model formalism. This presents a departure from classical sequential analysis, which originally focused on the inference of a signal change point. We also formulated and solved a change point detection problem for non-independent data. In particular, we studied the optimal detection and estimation of shift in the mean of Gaussian processes, and other weakly mixing processes, by introducing and proving optimality of our detection and estimation algorithms, which take into account the underlying dependence structure present in the data. In terms of modeling, we introduced a number of novel statistical models, whose applicability is extended beyond the setting of sensor networks applications. They include a class of graphical model based latent variable models for multiple change point detection. Motivated by the view of space and time as providing contextual anchors, we developed a class of Bayesian nonparametric hierarchical models which enable simultaneous clustering and coupling of data content and contextual information, thereby extending the applicability of the model to addressing other types of contextual inference other than notions of space and time. In terms of algorithms, we developed a new approximate, distributed and extremely fast sequential algorithm for inference in the multiple latent change-point graphical models. In attempting to understand the behavior of this algorithm, we discovered a new characterization of Bayesian posterior inference, from a computational viewpoint, as a performing a system of iterated random functions, a concept originated from applied probability. This viewpoint allows us to generalize approximate Bayesian inference as a class of iterated random functions, which are more amentable to improvement in computational efficiency and accuracy. We also developed sampling based algorithms for fitting the nonparametric Bayesian hierarchical models. In terms of theory, we developed an optimal theory for the multiple change point detection method based on graphical models, showing how the optimal detection error and delay times are characterized in terms of the underlying graphical structures. For the change point detection problem with Gaussian processes, we also established a minimax optimal theory for our method, and in particular showed how both the detection and estimation performance of such data depend on the underlying dependence structure given by the Gaussian covariance function. In another unexpected offshoot of the theoretical work, while attempting to understand the statistical behavior of latent variables in the proposed models, the PI was able to resolve several longstanding open questions in theoretical statistics, on the convergence of latent variables in Bayesian mixture and hierarchial models. The contributions described above have been published or due to appear in a number of top venues in statistics, information theory and machine learning. Broader impacts. The developments of novel models and algorithms are expected to be enrich not just the computational toolbox of sensor network modeling and algorithms, but also the broader fields of statistical modeling and machine learning with complex and spatiotemporal data. The connection of iterative random function systems and Bayesian inference has the potential to improve and open up interesting and new venues for fast Bayesian computation in statistical sciences. The statistical theory for latent variable models are starting to bear fruits, with useful implication to improved understanding and practice for practitioners in the data mining fields who work with large scale hierarchical models. The interdisciplinary nature of this project helps to train three graduate students and one postdoctral researcher from different research disciplines, helping to equipping them with broad knowledge and cross-disciplinary skills in the fields of computer science, statistics, signal processing and engineering. The algorithms, models and data obtained as part of this project have been used in a number of undergraduate and graduate level courses at the University of Michigan.
