  Most existing approaches to clustering gene expression time course data treat
the different time points as independent dimensions and are invariant to
permutations, such as reversal, of the experimental time course. Approaches
utilizing HMMs have been shown to be helpful in this regard, but are hampered
by having to choose model architectures with appropriate complexities. Here we
propose for a clustering application an HMM with a countably infinite state
space; inference in this model is possible by recasting it in the hierarchical
Dirichlet process (HDP) framework (Teh et al. 2006), and hence we call it the
HDP-HMM. We show that the infinite model outperforms model selection methods
over finite models, and traditional time-independent methods, as measured by a
variety of external and internal indices for clustering on two large publicly
available data sets. Moreover, we show that the infinite models utilize more
hidden states and employ richer architectures (e.g. state-to-state transitions)
without the damaging effects of overfitting.
