Products of Hidden Markov Models: It Takes N>1 to Tango
This work addresses computational bottlenecks for researchers using PoHMMs in time-series modeling, though it is incremental as it applies existing techniques to an underexplored model class.
The paper tackled the computational challenges of Products of Hidden Markov Models (PoHMMs) by using Annealed Importance Sampling to estimate the partition function and contrastive divergence learning on rainfall and dance data, suggesting PoHMMs are now viable for complex time-series modeling due to improved methods and computing power.
Products of Hidden Markov Models(PoHMMs) are an interesting class of generative models which have received little attention since their introduction. This maybe 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.