identification is the process of sensing the environment and using
these measurements to learn the equations which describe a system.
Existing approaches are unable to cope with the high-dimensionality,
nonlinearity, and structure found in autonomous systems, biology, and
other large networks. I will present a new statistical system
identification tool which tackles some of the challenging features of
these systems. This tool uses new statistical methods which we have
developed for performing regression on manifolds. Our method uses the
notion of exterior derivatives and cotangent spaces from differential
geometry to provide a new regularization technique for ill-posed
(weighted) linear regression problems. I will
give examples of system identification—for biological networks,
autonomous helicopters, and computer vision data—in which our tools
improve the identification of the system.