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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2017
- DOI:
- 10.48550/arXiv.1707.06756
- arXiv:
- arXiv:1707.06756
- Bibcode:
- 2017arXiv170706756R
- Keywords:
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- Statistics - Machine Learning;
- Computer Science - Artificial Intelligence;
- Computer Science - Machine Learning;
- Statistics - Methodology;
- G.3;
- I.2.6
- E-Print:
- 16 pages, 4 figures, accepted to ICML 2017, includes supplemental appendix