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Many real-valued stochastic time-series are locally linear (Gassian), butglobally non-linear. For example, the trajectory of a human hand gesture can beviewed as a linear dynamic system driven by a nonlinear dynamic system thatrepresents muscle actions. We present a mixed-state dynamic graphical model inwhich a hidden Markov model drives a linear dynamic system. This combinationallows us to model both the discrete and continuous causes of trajectories suchas human gestures. The number of computations needed for exact inference isexponential in the sequence length, so we derive an approximate variationalinference technique that can also be used to learn the parameters of thediscrete and continuous models. We show how the mixed-state model and thevariational technique can be used to classify human hand gestures made with acomputer mouse.

Variational Learning in Mixed-State Dynamic Graphical Models