Variational inference in a truncated Dirichlet process
The N -component truncated Dirichlet process (DPN ) is defined in Ishwaran and James [2001] and converges almost surely to a true Dirichlet process (DP∞). Like a full Dirichlet process, this distribution can be used as a nonparametric Bayesian prior in a mixture model. Ishwaran and James show that this approximation allows a blocking strategy in the corresponding Gibbs sampler which can be faster than the classical Gibbs samplers developed for the DP∞ prior [Escobar and West, 1995]. In this paper, we develop a variational inference algorithm to approximate the posterior in a Bayesian mixture model with a DPN prior. An exponential family mixture model with DPN prior on the natural parameter of the mixture component is illustrated in Figure 2. The random variables are distributed as follows: