A Note on the Implementation of Hierarchical Dirichlet Processes

The implementation of collapsed Gibbs samplers for non-parametric Bayesian models is non-trivial, requiring con-siderable book-keeping. Goldwater et al. (2006a) presented an approximation which significantly reduces the storage and computation overhead, but we show here that their formulation was incorrect and, even after correction, is grossly inaccurate. We present an alternative formulation which is exact and can be computed easily. However this approach does not work for hierarchical models, for which case we present an efficient data structure which has a better space complexity than the naive approach.