Bernal S D_2010.pdf - University of Plymouth

4.5. FEEDBACK PfiOCESSWG
t.(VJ,) jixdJ,) '^(UK)
kj, BlBtes
k,^ nuTnbur ofchild slates
k„ = numbfi- a( paienl stales
N - number of pareni nodes
•Simii ^ sampleil number of parent stales (max values)
N„,, sampled number iif pareni nodes (max variance)
P(Xl {Compatlbl«(U,)» 1
p- r-
1 ^ 1
1
1
1
1 1
^
N CPTs
P(X| {CompatiblttfUJ))
•-..
m [
^^^1
F^ ^
Choose only the maximum k„„,„, values from the N„,„ parent nodes with highest variance
• Reduces the number of operaliouK lo calculate Belief and messages
Figure 4. It: Sunipling of iht parcni n messugcs lo reduce ihe number of operations required
fur belief pnipagalinn. Only liie k„mni states, with the highesi values, from the
JVfluu Jt messages, wiili the highesi variance, are used in the talculatioii, where
Kim.\ < ku and A',na, < N. The states with the stronger response of the prnbabiliiy
distribuiions wiih higher varianee are likely lo carry most of the inrormaiioii
conleni of the parent JT messages. To ensure the belief calculations arc still valid
it is necessary to select ihe appropriate columns of the CPTs, i.e. those Ihai correspond
to ihe sampled siuies of ihc n messages. This reduces the number of
operations lo i^y^i^ sums and N^ax • ^S^^ product operations.
in the calculation, where ku,nax < K and Nmax < /V. The states with the stronger response of
the probability distributions with higher variance are likely to cany most of the information
conleni of Ihe pareni n messages. To ensure the belief calculations are still valid it is necessary
to select the appropriate columns of the CPTs. i.e. those that correspond to ihe sampled states of
Ihe 7t messages. This reduces the number of operations lo tj)^^;^', sums and /V„ • it^ product
operations. Figure 4.16 illustrates the sampling process. Although in this section we refer only
to the belief calculation, the same methtxl is applied to calculate the A messages, which also
integrate information from the parent nodes.
To check how well this sampling procedure managed to approximate the exact belief functions.
the method was tested statistically. Using randomly generated CPTs P{K\V\.- • • ,UM) and like-
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