Research in nonlinear dynamics in the last decade has led to a number of much more broadly applicable techniques for inferring the underlying unknown state of a system from accessible observables, and then building predictive models in the recovered state-space. I will discuss the relationship between state reconstruction and signal separation by time-delay embedding, and estimation by conventional linear filters. I will then look at how nonlinear dissipative entrainment can be applied to state estimation in coding problems, and the connection to recursive estimation. The talk will close with a description of Cluster-Weighted Modeling, a new framework for the associated inference problem for nonlinear stochastic data in high-dimensional spaces.

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1996-1997 Mathematics in High Performance Computing