  We propose dynamical systems trees (DSTs) as a flexible class of models for
describing multiple processes that interact via a hierarchy of aggregating
parent chains. DSTs extend Kalman filters, hidden Markov models and nonlinear
dynamical systems to an interactive group scenario. Various individual
processes interact as communities and sub-communities in a tree structure that
is unrolled 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 and
mediate the interaction between leaf processes or between other parent
processes in the hierarchy. Aggregator chains are parents of child processes
that they combine and mediate, yielding a compact overall parameterization. We
provide tractable inference and learning algorithms for arbitrary DST
topologies via an efficient structured mean-field algorithm. The diverse
applicability of DSTs is demonstrated by experiments on gene expression data
and by modeling group behavior in the setting of an American football game.
