Comparison and Bayesian Estimation of Feature Allocations

TL;DR

This paper introduces a novel Bayesian method for estimating feature allocations from posterior samples, utilizing a new loss function and an efficient algorithm to improve accuracy and flexibility.

Contribution

The paper proposes FARO loss and FANGS algorithm for Bayesian feature allocation estimation, enabling optimal point estimates beyond sampled allocations.

Findings

FARO loss satisfies quasi-metric properties for comparing feature allocations.

FANGS algorithm efficiently finds Bayes estimates by minimizing expected FARO loss.

Implementation available in the fangs R package.

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, 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.