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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