  We present a consensus Monte Carlo algorithm that scales existing Bayesian
nonparametric models for clustering and feature allocation to big data. The
algorithm is valid for any prior on random subsets such as partitions and
latent feature allocation, under essentially any sampling model. Motivated by
three case studies, we focus on clustering induced by a Dirichlet process
mixture sampling model, inference under an Indian buffet process prior with a
binomial sampling model, and with a categorical sampling model. We assess the
proposed algorithm with simulation studies and show results for inference with
three datasets: an MNIST image dataset, a dataset of pancreatic cancer
mutations, and a large set of electronic health records (EHR). Supplementary
materials for this article are available online.
