Open Access
September 2022 The Attraction Indian Buffet Distribution
Richard L. Warr, David B. Dahl, Jeremy M. Meyer, Arthur Lui
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Bayesian Anal. 17(3): 931-967 (September 2022). DOI: 10.1214/21-BA1279


We propose the attraction Indian buffet distribution (AIBD), a distribution for binary feature matrices influenced by pairwise similarity information. Binary feature matrices are used in Bayesian models to uncover latent variables (i.e., features) that explain observed data. The Indian buffet process (IBP) is a popular exchangeable prior distribution for latent feature matrices. In the presence of additional information, however, the exchangeability assumption is not reasonable or desirable. The AIBD can incorporate pairwise similarity information, yet it preserves many properties of the IBP, including the distribution of the total number of features. Thus, much of the interpretation and intuition that one has for the IBP directly carries over to the AIBD. A temperature parameter controls the degree to which the similarity information affects feature-sharing between observations. Unlike other nonexchangeable distributions for feature allocations, the probability mass function of the AIBD has a tractable normalizing constant, making posterior inference on hyperparameters straight-forward using standard MCMC methods. A novel posterior sampling algorithm is proposed for the IBP and the AIBD. We demonstrate the feasibility of the AIBD as a prior distribution in feature allocation models and compare the performance of competing methods in simulations and an application.

Funding Statement

This work was supported, in part, by NIH NIGMS R01 GM104972.


The authors thank the editor, associate editor, and two anonymous referees for their insightful comments that substantially improved this work.


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Richard L. Warr. David B. Dahl. Jeremy M. Meyer. Arthur Lui. "The Attraction Indian Buffet Distribution." Bayesian Anal. 17 (3) 931 - 967, September 2022.


Published: September 2022
First available in Project Euclid: 28 July 2021

arXiv: 2106.05403
MathSciNet: MR4505384
Digital Object Identifier: 10.1214/21-BA1279

Keywords: Bayesian nonparametric models , Chinese restaurant process , clustering , feature allocations , Indian buffet process , latent feature models

Vol.17 • No. 3 • September 2022
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