Learning Dynamical Systems

This group will consider statistical inference for dynamical systems. We interpret dynamical systems broadly as systems that evolve over time in a structured fashion, including in particular iterates of a measure preserving map, differential equations describing models of a physical system, and time varying social or communication networks. Some potential topics of interest:

* Parametric and non-parametric inference (in particular, estimation and testing) for dynamical systems problems under different observation (noise) models. Analogues of maximum likelihood and method of moments.
* Sufficient statistics for dynamical systems: low dimensional images of high-dimensional systems (or families of systems) whose dynamics capture features of the base system that are necessary for statistical inference.
* Modeling of, and inference from, dynamical networks; detection and assessment of longitudinal communities.
* Metrics between dynamical systems, especially those that provably capture differences between systems that are relevant for statistical inference.
* Metric and measure-based notions of complexity for families of dynamical systems; applications of complexity to learning and inference for families of systems with amenable mixing properties.