  Many real-valued stochastic time-series are locally linear (Gassian), but
globally non-linear. For example, the trajectory of a human hand gesture can be
viewed as a linear dynamic system driven by a nonlinear dynamic system that
represents muscle actions. We present a mixed-state dynamic graphical model in
which a hidden Markov model drives a linear dynamic system. This combination
allows us to model both the discrete and continuous causes of trajectories such
as human gestures. The number of computations needed for exact inference is
exponential in the sequence length, so we derive an approximate variational
inference technique that can also be used to learn the parameters of the
discrete and continuous models. We show how the mixed-state model and the
variational technique can be used to classify human hand gestures made with a
computer mouse.
