  The Indian buffet process (IBP) and phylogenetic Indian buffet process (pIBP)
can be used as prior models to infer latent features in a data set. The
theoretical properties of these models are under-explored, however, especially
in high dimensional settings. In this paper, we show that under mild sparsity
condition, the posterior distribution of the latent feature matrix, generated
via IBP or pIBP priors, converges to the true latent feature matrix
asymptotically. We derive the posterior convergence rate, referred to as the
contraction rate. We show that the convergence holds even when the
dimensionality of the latent feature matrix increases with the sample size,
therefore making the posterior inference valid in high dimensional setting. We
demonstrate the theoretical results using computer simulation, in which the
parallel-tempering Markov chain Monte Carlo method is applied to overcome
computational hurdles. The practical utility of the derived properties is
demonstrated by inferring the latent features in a reverse phase protein arrays
(RPPA) dataset under the IBP prior model. Software and dataset reported in the
manuscript are provided at http://www.compgenome.org/IBP.
