|Date: Friday, January 25, 2019
Location: 1084 East Hall (3:00 PM to 4:00 PM)
Title: Embedding and prediction of dynamical time series
Abstract: In this talk, we overview two aspects of the analysis of time series generated from dynamical systems: state space reconstruction and time series prediction. First, state space reconstruction consists of constructing representations of the states of an unknown dynamical system using the observed time series. Delay-time coordinates are commonly used for this purpose and have been shown to produce faithful representations of the state space for generic observation mechanisms. Motivated by common usage of delay-time coordinates, we consider the more difficult situation where the observation mechanism is fixed and genericity is studied with respect to perturbations of the dynamical system. Second, prediction of dynamical time series with observational noise using kernel-based regression has been shown to be consistent for certain classes of discrete dynamical systems. Nonetheless, these methods are only optimal when noise in the reconstructed states cannot be reduced. For continuous-time dynamical systems, we show that the use of smoothing splines to reduce noise before using kernel-based regression results in increased prediction accuracy, and analyze a setting for which such method consistently learns the exact predictor based on the noiseless time series.
Speaker: Raymundo Navarrete
Institution: University of Arizona
Event Organizer: AIM seminar organizers