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arXiv · 2409.01943

Spatially-dependent Indian Buffet Processes

Shonosuke Sugasawa·Daichi Mochihashi
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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.

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Shonosuke Sugasawa, Daichi Mochihashi. 2024-09-03. Spatially-dependent Indian Buffet Processes. https://arxiv.org/abs/2409.01943

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