Bernal S D_2010.pdf - University of Plymouth

4.5. FEEDBACK PROCESSING
lihood functions A(x), the difference between the exact beliefs and the approximated beliefs
obtained after sampling for different values of N^ax and kumax was measured. The difference
was measured using the Kullback-Leibler (K-L) divergence.
Figure 4.17 shows the K-L divergence between the real and approximate beliefs, averaged over
50 trials, as a function oiN^ax and Kmax- ''or comparison, the K-L divergence between the exact
belief and a randomly generated belief distribution is also plotted. The range over which these
parameters are tested is limited by the computational cost associated with calculating the exact
beliefs using CRTs of size exponential to the number of parents. Thus the chosen parameters
are kx - 10. A,/ = 20,N = 6, A:„^^, - {I •• -19} and A/,„„. - {I - - -6}.
The results show thai as A',^, and kumax increase, the goodness of hi between the approximation
and the exact belief increases. Furthermore, the relative difference between the K-L divergence
of the approximate and the random belief distributions suggests that even for relatively small
values of vV„„, and jkumo^r the approximate belief provides agood fit to the exact belief. The sam­
pling parameters have lo be chosen as a compromise between the accuracy of the approximation
and the computational cost.
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