  Diversity or complementarity of experts in ensemble pattern recognition and
information processing systems is widely-observed by researchers to be crucial
for achieving performance improvement upon fusion. Understanding this link
between ensemble diversity and fusion performance is thus an important research
question. However, prior works have theoretically characterized ensemble
diversity and have linked it with ensemble performance in very restricted
settings. We present a generalized ambiguity decomposition (GAD) theorem as a
broad framework for answering these questions. The GAD theorem applies to a
generic convex ensemble of experts for any arbitrary twice-differentiable loss
function. It shows that the ensemble performance approximately decomposes into
a difference of the average expert performance and the diversity of the
ensemble. It thus provides a theoretical explanation for the
empirically-observed benefit of fusing outputs from diverse classifiers and
regressors. It also provides a loss function-dependent, ensemble-dependent, and
data-dependent definition of diversity. We present extensions of this
decomposition to common regression and classification loss functions, and
report a simulation-based analysis of the diversity term and the accuracy of
the decomposition. We finally present experiments on standard pattern
recognition data sets which indicate the accuracy of the decomposition for
real-world classification and regression problems.
