PETS: Predicting efficiently using temporal symmetries in temporal probabilistic graphical models

Abstract

In Dynamic Bayesian Networks, time is considered discrete: In medical applications, a time step can correspond to, for example, one day. Existing temporal inference algorithms process each time step sequentially, making long-term predictions computationally expensive. We present an exact, GPU-optimizable approach exploiting symmetries over time for prediction queries, which constructs a matrix for the underlying temporal process in a preprocessing step. Additionally, we construct a vector for each query capturing the probability distribution at the current time step. Then, we time-warp into the future by matrix exponentiation. In our empirical evaluation, we show an order of magnitude speedup over the interface algorithm. The work-heavy preprocessing step can be done offline, and the runtime of prediction queries is significantly reduced. Therefore, we can handle application problems that could not be handled efficiently before.