Spatially-dependent Indian Buffet Processes

TL;DR

This paper introduces the spatially-dependent Indian buffet process (SIBP), a new stochastic process that models spatially correlated binary matrices, with applications demonstrated in linguistics and ecology.

Contribution

The paper proposes the SIBP, integrating spatial dependency into the IBP using Gaussian processes, and develops a Gibbs sampling algorithm for inference.

Findings

SIBP captures spatial correlation effectively in binary matrix data.

The model's properties are consistent with the original IBP in terms of non-zero entries.

Applications show SIBP's utility in analyzing linguistic and ecological spatial data.

Abstract

We develop a new stochastic process called spatially-dependent Indian buffet processes (SIBP) for spatially correlated binary matrices and propose general spatial factor models for various multivariate response variables. We introduce spatial dependency through the stick-breaking representation of the original Indian buffet process (IBP) and latent Gaussian process for the logit-transformed breaking proportion to capture underlying spatial correlation. We show that the marginal limiting properties of the number of non-zero entries under SIBP are the same as those in the original IBP, while the joint probability is affected by the spatial correlation. Using binomial expansion and Polya-gamma data augmentation, we provide a novel Gibbs sampling algorithm for posterior computation. The usefulness of the SIBP is demonstrated through simulation studies and two applications for large-dimensional multinomial data of areal dialects and geographical distribution of multiple tree species.