Research in LIDS in the areas of estimation, statistics, and learning has its roots in dynamical systems – e.g., estimation of the state of a dynamical system, or the identification of a dynamic model for such a system. While this remains one of the important contexts for our work in this area, the scope is now much broader, with an emphasis on the extraction of information about complex phenomena from complex and varied sources of data, the modeling and learning of the structure of such phenomena, and the subsequent use of the acquired information for estimation, optimization, and control.
In addition, in response to enabling technologies including wireless networks and sensor networks, our research also addresses the challenges of distributed implementation in power- and bandwidth-limited networks. A common thread in much of our research involves the development and analysis of algorithms that scale well to very large problem sizes, together with theoretical guarantees and performance bounds.
Some of the core methodological problems and challenges that are the subject of recent, current, or future work in LIDS include:
- The development of methods that identify and exploit structure for the cases of very large data sets and possibly moderate data sets that consist of high-dimensional data phenomena that can be described at various levels of granularity (multiscale and/or multiphysics models).
- The development of methods for inference in graphical models, together with improved understanding of existing but poorly understood methods (e.g., belief propagation), in conjunction with a cross-fertilization with statistical mechanics.
- The development of methods for compressing information in a manner tuned to a system’s end-objectives (e.g., compression in conjunction with data fusion, image and video compression, “compressed sensing”, decision-directed compression, etc.).
- The development of “active inference” methods, which include proactive choices of measurement modes in either static inference settings, or in “online learning” settings.
In addition, our research is tied to diverse applications, from the geosciences to sensor networks.