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Dynamical Systems Trees

Jebara, Tony; Howard, Andrew

We propose dynamical systems trees (DSTs) as a flexible model for describing multiple processes that interact via a hierarchy of aggregating processes. DSTs extend nonlinear dynamical systems to an interactive group scenario. Various individual processes interact as communities and sub-communities in a tree structure that is un-rolled in time. To accommodate nonlinear temporal activity, each individual leaf process is modeled as a dynamical system containing discrete and/or continuous hidden states with discrete and/or Gaussian emissions. Subsequent, higher level parent processes act like hidden Markov models that mediate the interaction between leaf processes or between other parent processes in the hierarchy. Aggregator chains are parents of the child processes the combine and mediate, yielding a compact overall parameterization. We provide tractable inference and learning algorithms for arbitrary DSTs topologies via structured mean field. Experiments are shown for real trajectory data of tracked American football plays where a DST tracks players as dynamical systems mediated by their team processes mediated in turn by a top-level game process.

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Academic Units
Computer Science
Publisher
Department of Computer Science, Columbia University
Series
Columbia University Computer Science Technical Reports, CUCS-028-03
Published Here
April 26, 2011