Products of Hidden Markov Models: It Takes N>1 to Tango

Products of Hidden Markov Models (PoHMMs) are an interesting class of generative models which have received little attention since their introduction. This may be in part due to their more computationally expensive gradient-based learning algorithm, and the intractability of computing the log likelihood of sequences under the model. In this paper, we demonstrate how the partition function can be estimated reliably via Annealed Importance Sampling. We perform experiments using contrastive divergence learning on rainfall data and data captured from pairs of people dancing. Our results suggest that advances in learning and evaluation for undirected graphical models and recent increases in available computing power make PoHMMs worth considering for complex time-series modeling tasks.