Detailed Derivations of Small-Variance Asymptotics for some Hierarchical Bayesian Nonparametric Models
arXiv:1501.00052v1
Originality Synthesis-oriented
AI Analysis
This work offers incremental derivations for researchers in Bayesian nonparametrics, clarifying technical aspects without introducing new methods.
The authors derived small-variance asymptotics for hierarchical Dirichlet process mixture models and hidden Markov models, providing detailed calculations for partition probabilities in Chinese restaurant processes and franchises.
In this note we provide detailed derivations of two versions of small-variance asymptotics for hierarchical Dirichlet process (HDP) mixture models and the HDP hidden Markov model (HDP-HMM, a.k.a. the infinite HMM). We include derivations for the probabilities of certain CRP and CRF partitions, which are of more general interest.