Title: An Infinite Hidden Markov Model With Similarity-Biased Transitions,
Abstract: We describe a generalization of the Hierarchical Dirichlet Process Hidden
Markov Model (HDP-HMM) which is able to encode prior information that state
transitions are more likely between "nearby" states. This is accomplished by
defining a similarity function on the state space and scaling transition
probabilities by pair-wise similarities, thereby inducing correlations among
the transition distributions. We present an augmented data representation of
the model as a Markov Jump Process in which: (1) some jump attempts fail, and
(2) the probability of success is proportional to the similarity between the
source and destination states. This augmentation restores conditional conjugacy
and admits a simple Gibbs sampler. We evaluate the model and inference method
on a speaker diarization task and a "harmonic parsing" task using four-part
chorale data, as well as on several synthetic datasets, achieving favorable
comparisons to existing models.