Bayesian Classifier Fusion with an Explicit Model of Correlation

TL;DR

This paper introduces a hierarchical Bayesian model for classifier fusion that explicitly models correlations between classifiers using a new correlated Dirichlet distribution, improving fusion performance in correlated settings.

Contribution

It proposes a novel correlated Dirichlet distribution within a hierarchical Bayesian framework for probabilistic classifier fusion, accommodating correlated classifiers explicitly.

Findings

Bayesian fusion can be Bayes optimal even with highly correlated classifiers.

The model generalizes classic independent opinion pooling methods.

Fusion performance improves with explicit correlation modeling.

Abstract

Combining the outputs of multiple classifiers or experts into a single probabilistic classification is a fundamental task in machine learning with broad applications from classifier fusion to expert opinion pooling. Here we present a hierarchical Bayesian model of probabilistic classifier fusion based on a new correlated Dirichlet distribution. This distribution explicitly models positive correlations between marginally Dirichlet-distributed random vectors thereby allowing explicit modeling of correlations between base classifiers or experts. The proposed model naturally accommodates the classic Independent Opinion Pool and other independent fusion algorithms as special cases. It is evaluated by uncertainty reduction and correctness of fusion on synthetic and real-world data sets. We show that a change in performance of the fused classifier due to uncertainty reduction can be Bayes optimal even for highly correlated base classifiers.