The multivariate probit Indian buffet process

Stolf Federica, University of Padova

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 as in a multivariate probit fashion. We show that the proposed approach preserves many theoretical appealing properties of the IBP. For posterior computations we propose different approaches to effectively reduce the dimensionality of the correlation matrix and obtain efficient scalability to high dimensions. Simulation studies and applications to fungal biodiversity data provide support for the new modeling class relative to competitors.

Area: CS15 - Recent Advances in Bayesian Nonparametric Statistics (Marta Catalano and Beatrice Franzolini)

Keywords: Indian buffet process, Multivariate probit

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