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Activity Number: 245 - Bayesian Models for Clustering and Latent Allocation
Type: Contributed
Date/Time: Tuesday, August 9, 2022 : 8:30 AM to 10:20 AM
Sponsor: Section on Bayesian Statistical Science
Abstract #323594
Title: Search Algorithms and Loss Functions for Bayesian Feature Allocation Models
Author(s): Robert Jacob Andros* and David B. Dahl and Devin Johnson
Companies: Brigham Young University and Brigham Young University and Duke University
Keywords: Bayesian nonparametrics; Indian buffet process; Linear assignment problem; Hamming distance

Feature allocation models postulate a sampling distribution whose parameters are derived from shared features. Bayesian models place a prior distribution on the feature allocation and Markov chain Monte Carlo is typically used for model fitting, resulting in thousands of feature allocations sampled from the posterior distribution. We propose a method to estimate a latent feature allocation based on these samples. First, we introduce FARO loss, a function between feature allocations which satisfies quasi-metric properties and allows for comparing feature allocations with differing numbers of features. The loss involves finding the optimal feature ordering among all possible, but computational feasibility is achieved by framing this task as a linear assignment problem. We also introduce the FANGS algorithm to obtain a Bayes estimate by minimizing the Monte Carlo estimate of the posterior expected loss using the available samples. FANGS can produce an estimate other than those visited in the Markov chain. We provide an investigation of existing methods and our proposals. Our loss function and search algorithm are implemented in the fangs package for R, available on CRAN.

Authors who are presenting talks have a * after their name.

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