Bernal S D_2010.pdf - University of Plymouth

4.3. LEARNING
4.3 Learning
This section describes how to learn the conditional probability tables (CPTs) of each of the
nodes in the Bayesian network in order to approximate the selectivity and invariance operations
of the HMAX model. For this learning stage an important assumption is made in order to
simplify the process. The network is assumed have a single parent per node (tree stracture
with no loops) so that the feedforward A messages are not affected by the top-down feedback n
messages. The bottom-up A message from a node with a single parent does not include evidence
from that parent (see Section 3.3.3 for details).
The reason for making this assumption is that the CPTs in the network are learned in an unsu­
pervised manner, starling from the bottom layer (following HMAX learning methcxls), based
on the response obtained at each layer. In order to calculate the response of nodes with multiple
parents, the messages from all parents need lo be combined using the CPTs thai relate the node
lo its parents. However, these CPTs would still be unknown. This implie-s that, theoretically.
in this type of network, all the CPTs would need to be learned at the same time. By assuming
nodes with a single parent, the A messages, based solely on bottom-up evidence, can be used
as a reference to learn the appropriate weights layer by layer. Similar assumptions are made in
other related models (Hpshtein et al. 2008, George and Hawkins 2009. Hinton ct al. 2006). The
learning process is now described one layer at a lime.
4.3.1 Image-Si weights
The input image is pre-processed with a battery of Gabor filters described by Equation (4.1)
with the parameter range described in Table 4.1, i.e. at 4 different orientations and 8 sizes. Each
of the lilters is applied at every location of the image. The filtered responses, normalized over
the four orientations at each location and scale, are used as the output A messages of a set of
dummy nodes that feed onto the SI nodes. As explained in Section 3.3.3. dummy nodes do not
encode a variable or have a belief, but just generate k messages for the parent niRies. For this
reason there is no need lo define the Cl^s between the dummy nodes and the SI nodes.
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