TY - JOUR
T1 - Homogeneous functionals and Bayesian data fusion with unknown correlation
AU - Taylor, Clark N.
AU - Bishop, Adrian N.
N1 - Publisher Copyright:
© 2018
PY - 2019/1
Y1 - 2019/1
N2 - 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.
AB - 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.
KW - Consensus
KW - Conservative estimators
KW - Data fusion
KW - Distributed data fusion
UR - http://www.scopus.com/inward/record.url?scp=85043290998&partnerID=8YFLogxK
U2 - 10.1016/j.inffus.2018.02.002
DO - 10.1016/j.inffus.2018.02.002
M3 - Article
SN - 1566-2535
VL - 45
SP - 179
EP - 189
JO - Information Fusion
JF - Information Fusion
ER -