  Completely random measures provide a principled approach to creating flexible
unsupervised models, where the number of latent features is infinite and the
number of features that influence the data grows with the size of the data set.
Due to the infinity the latent features, posterior inference requires either
marginalization---resulting in dependence structures that prevent efficient
computation via parallelization and conjugacy---or finite truncation, which
arbitrarily limits the flexibility of the model. In this paper we present a
novel Markov chain Monte Carlo algorithm for posterior inference that
adaptively sets the truncation level using auxiliary slice variables, enabling
efficient, parallelized computation without sacrificing flexibility. In
contrast to past work that achieved this on a model-by-model basis, we provide
a general recipe that is applicable to the broad class of completely random
measure-based priors. The efficacy of the proposed algorithm is evaluated on
several popular nonparametric models, demonstrating a higher effective sample
size per second compared to algorithms using marginalization as well as a
higher predictive performance compared to models employing fixed truncations.
