PETS: Predicting Efficiently Using Temporal Symmetries in Temporal PGMs

Time in Bayesian Networks is concrete: In medical applications, a timestep can correspond to one second. To proceed in time, temporal inference algorithms answer conditional queries. But the interface algorithm simulates iteratively into the future making predictions costly and intractable for applications. We present an exact, GPU-optimizable approach exploiting symmetries over time during answering prediction queries by constructing a matrix for the underlying temporal process. Additionally, we construct a vector capturing the probability distribution at the current timestep. Then, we can time-warp into the future by matrix exponentiation. 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. Now, we can handle application problems that could not be handled before.