Variational Learning in Mixed-State Dynamic Graphical Models

TL;DR

This paper introduces a mixed-state dynamic graphical model combining hidden Markov models and linear dynamic systems, with a variational inference method for efficient approximation, applied to human gesture classification.

Contribution

It proposes a novel mixed-state model for time-series that captures both discrete and continuous dynamics, along with a variational inference technique for learning and inference.

Findings

Effective gesture classification using the mixed-state model.

The variational inference method enables scalable learning.

Model captures complex real-world time-series behaviors.

Abstract

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.