Bernal S D_2010.pdf - University of Plymouth

4.5. FEEDBACK PROCESSING
4.5.3 Loops In the network
4^.3.1 Dynamic etjuations
Due to the overlap between the RF of nodes at all layers, the resulting Bayesian network has
a large number of loops. As was described in Section ,1..1.5, in Bayesian networks without
loops belief propagation ohiains the exacl marginal probability distributions of all nodes after
a set number of iterations. However, if the network has loops, the original belief propagation
algorithm is no longer valid and approximate methods have to be implemented. The melhtxl
selected for this model is loopy belief propagation, which has been empirically demonstrated
to obtain good approximations to the exact beliefs in pyramidal networks (similar to that of the
model) once the approximate beliefs have converged after several iterations (Weiss 2000).
The fact that belief propagation now requires several iterations means that a temporal dimension
must be added to the original formulation. The resulting dynamical model is captured by the
set of Equations 4.11. These also include the weighted sum method described in Section 3.3.4
to approximate the combinalion of lop-down Jr messages.
^'"'w- n ^,w
J~-\..M
HI UK 8 i=i..fj
X U] uiv\u, k-t-NXi
ui UN\U, \ S / k----\..N\i
183
(4.11)