An Infinite Hidden Markov Model With Similarity-Biased Transitions
This work addresses the need for more flexible state transition modeling in probabilistic models, particularly for applications like audio analysis, though it is incremental as it builds on the HDP-HMM framework.
The authors tackled the problem of incorporating prior knowledge about state proximity into hidden Markov models by developing a generalization of the HDP-HMM that biases transitions based on state similarity, achieving favorable results in tasks like speaker diarization and harmonic parsing compared to existing models.
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.