Bernal S D_2010.pdf - University of Plymouth

4.6. SUMMARY OF MODEL APPROXIMATIONS TO BAYESIAN HEUEF PROPAGATION
node instead of on the likelihood funciion, A(X). This allows Ihe A messages lo be modulated
by top-down feedback even in regions that have initially flat distribulions, such as the missing
contours in the Kanizsa figure. This modification is shown in Rqualion (4.! 2).
4''("/)-Pl
4.6 Summary of model approximations to Bayesian belief propagation
• l-'eedforward recognition results assume a singly-connected tree-structured network (no
loops and one parent per node) so the HMAX operations can be approximated by the
propagation of bottom-up X messages. Similar approaches have been used in other relaied
models (Kpshtein et al. 2(X)8. tJcorge and Hawkins 20()'J, Hinlon ei ai. 2006). Preliminary
results suggest a similar invariani recognilion performance can be obtained even when
including the feedback K messages (loopy belief propagation), but the computational
cost associated precludes a comprehensive systematic test over the complete dataset and
parameter space.
• The number of input Af,(-r) messages used to compute the hkelihood function X{x) is
hmited to M^ai- in order to prevent the result of the product operalion from being outside
of Matlab's numeric range. The method has been empirically demonstrated to provide a
relatively good fit to the exact distribution given a moderate value of Mmax-
• The A and ;r messages are sum-normalized to 1 and then re-weighted so that the minimum
value of the distribution is equal V„i„ — 1/(^/10). This prevents extremely low values
leading to out of range solulions during the belief propagalion operations. The overall
shape of the distribution remains identical, except for some of the elements with smaller
values, which may now exhibit a relatively larger value. However. Ihe states with lowest
values are less likely lo affect the final resuh in a significant way and many of ihem will
be discarded anyway during the sampling methods implemented.
• The Ji messages are approximated by the belief al each mxle. The same approach is
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