Modeling Multiple-Mode Systems with Predictive State Representations

Predictive state representations (PSRs) are a class of models that represent the state of a dynamical system as a set of predictions about future events. This work introduces a class of structured PSR models called multi-mode PSRs (MMPSRs), which were inspired by the problem of modeling traffic. In general, MMPSRs can model uncontrolled dynamical systems that switch between several modes of operation. An important aspect of the model is that the modes must be recognizable from a window of past and future observations. Allowing modes to depend upon future observations means the MMPSR can model systems where the mode cannot be determined from only the past observations. Requiring modes to be defined in terms of observations makes the MMPSR different from hierarchical latent-variable based models. This difference is significant for learning the MMPSR, because there is no need for costly estimation of the modes in the training data: their true values are known from the mode definitions. Furthermore, the MMPSR exploits the modes’ recognizability by adjusting its state values to reflect the true modes of the past as they become revealed. Our empirical evaluation of the MMPSR shows that the accuracy of a learned MMPSR model compares favorably with other learned models in predicting both simulated and real-world highway traffic.