Bernal S D_2010.pdf - University of Plymouth

6.1. ANALYSIS OF RESULTS
The bclier propagation algorithm in Bayesian networks is. theoretically, well-suited to imple­
ment these horizontal interactions. Pearl (1988), the HrsI to lormulate belief propagation in
Bayesian networks, refers to them as sideways Interactions (see Section 3.3.3). Although there
are no explicit lateral connections, these are implemented implicitly by the bottom-up messages
and top-down messages, both of which take into account evidence from nodes adjacent to the
target. There are several possible reasons why, despite this, ihu results in Figure 5.25 (clamp­
ing of K{S2) to square representation) don't show signilicant contextual lateral interactions and
feedback disambiguation:
1. A number of approximations to the exact implementation of belief propagation have been
made (see Section 4,6). These include sampling methods that limit the messages to rel­
atively few samples which contain the highest information content. However, all the in­
formation that is lost due to the sampling and approximations might actually be required
for precise feedback disambiguation, hor example, features that present relatively low
probabilities and could potentially be enhanced by feedback might be initially discarded
during sampling,
2, All features belonging to the same group in complex layers are modulated equivalcntly
by feedback. Features within groups contain the precise and high resolution information
that could lead to belief refinement. As previously argued, allowing feedback to modulate
features within a group disparalely would lead to the enhancement of specific SI spatial
arrangements. This could be done by learning distinct weights for each feature or by
allowing features to belong lo different groups, both of which methods are implemented
in the HTM mode (George and Hawkins 2009).
i. Loopy belief propagation might require more time steps to converge to a good approxi­
mation of the exact belief. Current simulations run for a limited number of time steps due
to the high computational cost. Although beliefs tend lo show a relatively high degree of
convergence, it is possible that they are settling on local minima.
4, Beliefs are likely to evolve and be relined as a consequence of the hierarchical interactions
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