Comparison and Bayesian Estimation of Feature Allocations

ABSTRACT

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, which results in thousands of feature allocations sampled from the posterior distribution. Based on these samples, we propose a method to provide a point estimate of a latent feature allocation. 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 orderings, 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 FARO 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 proposed methods. Our loss function and search algorithm are implemented in the fangs package in R.

KEYWORDS:

• Bayesian nonparametrics
• Hamming distance
• Indian buffet process
• Linear assignment problem

Disclosure Statement

The authors report there are no competing interests to declare.

Notes

1 This should not be confused with the definition of generalized Hamming distance given by Bookstein, Kulyukin, and Raita (2002) in the computer science literature to compare bitmaps and bitstrings.

2 In the DFA study, Z followed a complex structure with six features. Some information in the first two features was treated as fixed, so we ignore these first two features and assume $K=4$.