Combinatorial Clustering and the Beta Negative Binomial Process

摘要: We develop a Bayesian nonparametric approach to general family of latent class problems in which individuals can belong simultaneously multiple classes and where each be exhibited times by an individual. introduce combinatorial stochastic process known as the negative binomial ( ${\rm NBP}$ ) infinite-dimensional prior appropriate for such problems. show that is conjugate beta process, we characterize posterior distribution under beta-negative BNBP}$ hierarchical models based on (the HBNBP}$ ). study asymptotic properties three-parameter extension exhibits power-law behavior. derive MCMC algorithms inference , present experiments using these domains image segmentation, object recognition, document analysis.