Learning and inference algorithms for partially observed structured switching vector autoregressive models

We present learning and inference algorithms for a versatile class of partially observed vector autoregressive (VAR) models for multivariate time-series data. VAR models can capture wide variety of temporal dynamics in a continuous multidimensional signal. Given a sequence of observations to be modeled by a VAR model, it is possible to estimate its parameters in closed form by solving a least squares problem. For high dimensional observations, the state space representation of a linear system is often invoked. One advantage of doing so is that we model the dynamics of a low dimensional hidden state instead of the observations, which results in robust estimation of the dynamical system parameters. The commonly used approach is to project the high dimensional observation to the low dimensional state space using a KL transform. In this article, we propose a novel approach to automatically discover the low dimensional dynamics in a switching VAR model by imposing discriminative structure on the model parameters. We demonstrate its efficacy via significant improvements in gesture recognition accuracy over a standard hidden Markov model, which does not take the state-conditional dynamics of the observations into account, on a bench-top suturing task.