The Attraction Indian Buffet Distribution

Abstract

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.

Comparison and Bayesian Estimation of Feature Allocations

“…Gershman et al (2015) proposed using the maximum a posteriori (MAP) feature allocation in the context of the distance dependent Indian Buffet Process (ddIBP). Warr et al (2021) successfully implemented this method in a classification study of Alzheimer's disease neuroimaging. Xu et al (2015) devised an objective function, similar to a penalized likelihood function, to find the MAP.…”

“…The studies discussed in the previous section included the simulations from the AIBD paper (Warr et al, 2021), the cytometry data model (Lui et al, 2021), and the DFA model for patient-disease relationships (Ni et al, 2020b). The loss functions in these studies were different; the first used zero-one loss, the second used a sum of squares function on the PSM, and the last used Hamming distance.…”

“…DFA (Ni et al, 2020b) 300 4 500 CMC (Ni et al, 2020a) 800 5 500 SIFA (Zeng et al, 2018) 80 6 4000 AIBD (Warr et al, 2021) 20 3 1000 Alzheimer's (Warr et al, 2021) 62 77 3000…”

“…Of the five sets of posterior feature allocation samples examined, two of them are from Warr et al (2021) and were already used in Section 4 (a smaller set simulated directly from their linear latent feature model and a larger set from real Alzheimer's disease data). In addition, we have samples from the CMC study (Ni et al, 2020a), the SIFA study (Zeng et al, 2018), and scenario 1 of the DFA model (Ni et al, 2020b) 2 .…”

“…Feature allocations have been used for a wide range of applications, most frequently in biostatistics. Such applications include disease classification (Warr et al, 2021), cell subpopulation identification (Lui et al, 2021), tumor heterogeneity inference (Xu et al, 2015), and symptom-disease relationship modeling (Ni et al, 2020b). These same studies have also explored methods for sampling feature allocations using MCMC.…”