  There is a rich literature on infinite latent feature models, with much of
the focus being on the Indian Buffet Process (IBP). The current literature
focuses on the case in which latent features are generated independently, so
that there is no within-sample dependence in which features are selected.
Motivated by ecology applications in which latent features correspond to which
species are discovered in a sample, we propose a new class of dependent
infinite latent feature models. Our construction starts with a probit Indian
buffet process, and then incorporates dependence among features through a
correlation matrix in a latent multivariate Gaussian random variable. We show
that the proposed approach preserves many appealing theoretical properties of
the IBP. To address the challenge of modeling and inference for a
growing-dimensional correlation matrix, we propose Bayesian modeling approaches
to reduce effective dimensionality. We additionally describe extensions to
incorporate covariates and hierarchical structure to enable borrowing of
information. For posterior inference, we describe Markov chain Monte Carlo
sampling algorithms and efficient approximations. Simulation studies and
applications to fungal biodiversity data provide compelling support for the new
modeling class relative to competitors.
