A fundamental challenge in engineering and science today is that systems contain tremendous numbers of interconnected components with complex interactions. Examples include communication and sensor networks, high-dimensional medical images, or biological systems such as vast sets of interconnected spiking neurons responding to a large array of stimuli. Graphical models provide a probabilistic framework for modeling such systems, and contemporary message-passing algorithms lead to computationally feasible operations by decomposing problems on larger systems into smaller ones. This research develops a broader methodology and new algorithms to address larger classes of more complex nonlinear interconnected systems with potential for great technological impact. For wider dissemination, this is coupled with educational initiatives including developing courses combining perspectives in signal processing, machine learning, and statistics in the context of modern applications. An open-source code base will foster cross-disciplinary research in students, educators, and industry.
This research combines the power of high-dimensional graphical models with recent advances in random systems theory to tackle a much wider scope of problems than traditional message-passing or linear methods allow. The investigator addresses the key gaps in scalable estimation and model inference for structured nonlinear systems and develops powerful general algorithms for solving core problems. Four main objectives address aspects of this broader goal: (i) systematic general methods for representing systems characterized by arbitrary interconnections of linear and nonlinear components; (ii) computationally scalable message-passing algorithms for estimation; (iii) rigorous quantification of high-dimensional performance; and (iv) validation of the methods on real data, including neurological system identification. These research thrusts greatly expand the scope of statistical estimation techniques and provide a rigorous approach to large-scale signal processing problems underlying the big data technology of today.
