Homogeneous functionals and Bayesian data fusion with unknown correlation

Clark N. Taylor*, Adrian N. Bishop

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)

Abstract

Information or data fusion concerns the aggregation, or combination, of probability measures. For example, in machine learning, statistics and signal processing, one may seek to ‘combine’ posterior distributions, [e.g. 1) Bayes classifiers or 2) posteriors over target states etc], arising from distinct but not necessarily independent sources. For example, sources might include partially disjoint trainers, or spatially distinct sensors correlated via state dependent measurements, etc. Data fusion is common in risk analysis where one is broadly interested in pooling expert opinions described by probability measures, and where it is often hard to assess and account for correlation among experts. The contribution of this work is the introduction of a broad class of data fusion rules that seek the combination of two (or more) probability distributions in the presence of non-zero, but unknown, correlation. We introduce rules that are improved in the sense that they are ‘closer’ to the true Bayesian result that would be computed if one could exploit knowledge of the correlation between the input distributions. We introduce these rules under the common algorithmic constraint of avoiding the so-called ‘double-counting’ of correlated information. The general framework proposed is based on homogeneous functionals. We examine the fusion performance and computational properties when using these functionals. We also consider distributed data fusion on (possibly) time-varying and incomplete network topologies and related convergence properties.

Original languageEnglish
Pages (from-to)179-189
Number of pages11
JournalInformation Fusion
Volume45
DOIs
Publication statusPublished - Jan 2019
Externally publishedYes

Fingerprint

Dive into the research topics of 'Homogeneous functionals and Bayesian data fusion with unknown correlation'. Together they form a unique fingerprint.

Cite this