Bernal S D_2010.pdf - University of Plymouth

4.J. HMAX AS A BAYESJAN m-TWORK
The first step in this process is to define the equivalences between the HMAX model and the
proposed Bayesian network. These are summed up in Figure 4.1 and are as follows:
1. Each node of the Bayesian network represents a specific location, band and layer of ihe
HMAX model.
2. The discrete states of each node of the Bayesian network represent the different feuiures
coded al thai location, band and layer of the HMAX model. For example each Bayesian
node at layer SI will have Ks\(- 4) features, representing the four different filler orien­
tations of HMAX.
3. The discrete probability distribution over the slates of each Bayesian node represents
the sum-normalized responses of the HMAX units coding the different features ai that
location, band and layer. Therefore, the probability distriliution of each node comprises
the response of K HMAX units, where K is the number of different features ai that layer.
4. The conditional probability tables (CPTs) that link each node in the Bayesian network
with its parent nodes in the layer above represent the prototype weights used lo implc-
menl selectivity in the HMAX model. Additionally, die CPTs are used to approximate
the max (invariance) operation between simple and complex layers of the HMAX model.
Learning the appropriate CPT parameters allows the model to approximate the HMAX
functionality during the inference stage (using belief propagation) of the Bayesian net­
work. This is described in further detail in Section 4.3.
Each node in the network implements the belief propagation algorithm, which has been de­
scribed in detail in .Section 3..1,3, ['igures 4.2 and 4.3 show the specific operations implemented
by each node, in the case of a single parent structure and a multiple parent structure, respec­
tively. The former corresponds lo a parlicularization of the latter. The operations performed
correspond to Hquations (3,27) to (3,31). The diagrams illustrate how to effectively implement
belief propagation in a local and distributed manner. Note that to do this the top-down output
messages of the node are made equivalent to the belief of the node. Therefore, the incoming
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