A New Modeling Framework for Continuous, Sequential Domains

Temporal models such as Dynamic Bayesian Networks (DBNs) and Hidden Markov Models (HMMs) have been widely used to model time-dependent sequential data. Typically, these approaches limit focus to discrete domains, employ first-order Markov and stationary assumptions, and limit representational power so that efficient (approximate) inference procedures can be applied. We propose a novel temporal model for continuous domains, where the transition distribution is conditionally tractable: it is modelled as a tractable continuous density over the variables at the current time slice only, while the parameters are controlled using a Recurrent Neural Network (RNN) that takes all previous observations as input. We show that, in this model, various inference tasks can be efficiently implemented using forward filtering with simple gradient ascent. Our experimental results on two different tasks over several real-world sequential datasets demonstrate the superior performance of our model against existing competitors.