Abstract

Hidden Markov models (HMMs) are one of the most widely used statistical models for time series. Traditionally, HMMs have a known structure with a fixed number of states and are trained using maximum likelihood techniques. The infinite HMM (iHMM) allows a potentially unbounded number of hidden states, letting the model use as many states as it needs for the data (Beal, Ghahramani and Rasmussen 2002). Teh, Jordan, Beal and Blei (2006) showed that a form of the iHMM could be derived from the Hierarchical Dirichlet Process, and described a Gibbs sampling algorithm based on this for the iHMM. I will talk about recent work we have done on infinite HMMs. In particular: we now have a much more efficient inference algorithm based on dynamic programming, called ‘Beam Sampling’, which should make it possible to apply iHMMs to larger problems. We have also developed a factorial version of the iHMM which makes it possible to have an unbounded number of binary state variables, and can be thought of as a time-series generalization of the Indian buffet process.

Joint work with Jurgen van Gael (Cambridge), Yunus Saatci (Cambridge) and Yee Whye Teh (Gatsby Unit, UCL ).