Hidden markov models with stick-breaking priors

John Paisley, Lawrence Carin

Research output: Contribution to journalArticlepeer-review

51 Scopus citations


The number of states in a hidden Markov model (HMM) is an important parameter that has a critical impact on the inferred model. Bayesian approaches to addressing this issue include the nonparametric hierarchical Dirichlet process, which does not extend to a variational Bayesian (VB) solution. We present a fully conjugate, Bayesian approach to determining the number of states in a HMM, which does have a variational solution. The infinite-state HMM presented here utilizes a stick-breaking construction for each row of the state transition matrix, which allows for a sparse utilization of the same subset of observation parameters by all states. In addition to our variational solution, we discuss retrospective and collapsed Gibbs sampling methods for MCMC inference. We demonstrate our model on a music recommendation problem containing 2250 pieces of music from the classical, jazz, and rock genres. © 2009 IEEE.
Original languageEnglish (US)
Pages (from-to)3905-3917
Number of pages13
JournalIEEE Transactions on Signal Processing
Issue number10
StatePublished - Oct 9 2009
Externally publishedYes

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