  Using the maximum entropy method, we derive the "adaptive cluster expansion"
(ACE), which can be trained to estimate probability density functions in high
dimensional spaces. The main advantage of ACE over other Bayesian networks is
its ability to capture high order statistics after short training times, which
it achieves by making use of a hierarchical vector quantisation of the input
data. We derive a scheme for representing the state of an ACE network as a
"probability image", which allows us to identify statistically anomalous
regions in an otherwise statistically homogeneous image, for instance. Finally,
we present some probability images that we obtained after training ACE on some
Brodatz texture images - these demonstrate the ability of ACE to detect subtle
textural anomalies.
