Bernal S D_2010.pdf - University of Plymouth

4.5. F^mSACK PRCKESSING
n^
(U,) i^(U,)
k„ stales
i.ifit^w
k,, states
k,states
I,(UN)
i..tii,ltMW
k„ states
k,- number of child slates
ku = number parent stales
N - number of parent nodes
• k, • kj^ CPT parameters to learn (cxponviitial)
e.g. 4-4" 262,144
• Belief ealculation performs kj^ sums and N • kj^ product operations {cxponetitial)
Bei(x)=nv(x)i'''i:Vp(xiu u.)f'fr7T.(u,)'
N^ ^rf
Figure 4.14: I'roblL-ms associated wiih ihc exponential dependency on the number of parent
nodes. As described in Section 3..1.4, the number of elements of the CPT
P\X^V\,--- ,UN) is exponential to the number of parents. N. as it includes entries
lor all possible combinations of the stales in node X and its parent nodes,
e.g. given *x = i(7 = 4,W = 8, the number of paramelcrs in the CPT is 4 • 4* =
262,144, Addilion;illy, Ihe number of operations tocompulc the belief is also exponeniiyl
to the number of purenis, more precisely, ii requires t;) sums and A'A^
product operations.
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