Bayesian Time Series Structure Learning: Formulation of an Event Driven Prior Distribution

Abstract

We study the prior distribution over structures of a Bayesian time series structure learning model—the Temporal Interaction Model (TIM) of Siracusa and Fisher III. We develop a new method for setting the hyperparameters of the TIM structure prior. Our contribution enables more consistent inference performance as the number of interacting nodes in the time series increases, which we show analytically and with synthetic experiments. Secondly, we prove that the form of the prior distribution is within the curved exponential family. Finally, we test our developments empirically. Because traffic dynamics are comparatively accessible to common knowledge, we choose traffic time series as a test case to examine general behaviors of TIM inference and in particular our parameterization of the structure prior.