  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, 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.
