Bernal S D_2010.pdf - University of Plymouth

4.7. ORIGINAL CONTRIBUTIONS IN THIS CHAPTER
used by IJtvak and Ullmaii (2009). George and Hawkins (2009). This approximalion is
justified when the total number of incoming messages to a node is relatively high, as is
the case of the present model
• The CPT P{X |t/i, • . Ufj) is approximated as the weighted sum of N CPTs of the form
f'{X\Ui). The method has been justified geometrically as providing a good model of the
combination of information from multiple experts {parent nodes) and has been success­
fully employed on other probabilistic models thai require reasoning under uncertainty
(Das 2004).
• For the calculation of the belief and the A messages, only ki„„ax highest-valued samples
from ihc N,„a, ^ messages with the highest variance are employed. The method has been
empirically demonstrated In provide a relatively good til to die exact distribution, given
moderate values o( N„aj i"id ^umai-
• To avoid the excessive computational cost associated to updating the beliefs and output
messages of the nodes in all layers, beliefs are for a single layer at each time step, starl­
ing from the bottom layer and moving upwards sequentially. The rationale behind this
approximation to loopy belief propagation is that evidence arrives at Ihe network from
dummy nodes connected to the bottom layer.
4.7 Original contributions in tliis chapter
• A Bayesian network that captures the structure of the HMAX model, a hierarchical object
recognition model based on anatomical and physiological cortical data.
• An approximalion to the selectivity and invariance operations of Ihe HMAX model using
the belief propagation algorithm over ihe proposed Bayesian network.
• An inherent extension of the static feedforward HMAX model to include dynamic and
recursive feedback ba.sed on the loopy belief propagation algorithm.
• A particularization of the CPT learning method proposed by Das (2004) to the hierarchi­
cal object recognition domain. The method simplifies the generation of the CPT parame-
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