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cs-677sp2010:clique-trees [2014/12/11 23:35]
ryancha
cs-677sp2010:clique-trees [2014/12/11 23:36] (current)
ryancha
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 Fig.5 Message passing Fig.5 Message passing
  
-In Fig.5, for example, the clique $C_2(G,​I,​D)$ ​ generates a factor ( message ) by multiplying the message$\delta_{1 \overrightarrow ​2}(D)$ ​  from $C_1$  with its initial potential $\pi^0_2(G,​I,​D)$ ​ and then summing out the variable D. The resulting factor ( message ) which has a scope G, I, is then sent to clique $C_3(G,​S,​I)$ .+In Fig.5, for example, the clique $C_2(G,​I,​D)$ ​ generates a factor ( message ) by multiplying the message$\delta_{1 \rightarrow ​2}(D)$ ​  from $C_1$  with its initial potential $\pi^0_2(G,​I,​D)$ ​ and then summing out the variable D. The resulting factor ( message ) which has a scope G, I, is then sent to clique $C_3(G,​S,​I)$ .
  
 We say that a clique is ''​ready''​ when it has received all of its incoming messages. Thus, in this example, we could see that $C_4$ is ''​ready''​ at the very start of the algorithm, and the computation associated with it can be performed at any point in the execution. We say that a clique is ''​ready''​ when it has received all of its incoming messages. Thus, in this example, we could see that $C_4$ is ''​ready''​ at the very start of the algorithm, and the computation associated with it can be performed at any point in the execution.
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 ===Calibrated Clique Tree=== ===Calibrated Clique Tree===
-* Define a term, belief ​ $\beta_i(C_i)=\pi^0_i \prod_{k \in Nb_i} \delta_{k \overrightarrow ​i}  $+* Define a term, belief ​ $\beta_i(C_i)=\pi^0_i \prod_{k \in Nb_i} \delta_{k \rightarrow ​i}  $
 * Two adjacent cliques $C_i$  and $C_j$  are said to be ''​calibrated''​ if $\sum_{C_i - S_{i,j}} \beta_i(C_i) = \sum_{C_j - S_{i,j}} \beta_j(C_j)$ ​ * Two adjacent cliques $C_i$  and $C_j$  are said to be ''​calibrated''​ if $\sum_{C_i - S_{i,j}} \beta_i(C_i) = \sum_{C_j - S_{i,j}} \beta_j(C_j)$ ​
 * A clique tree is ''​calibrated''​ if all pairs of adjacent cliques are ''​calibrated''​. * A clique tree is ''​calibrated''​ if all pairs of adjacent cliques are ''​calibrated''​.
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 An alternative approach to computing the message is to multiply in all of the messages and then divide the resulting factor by returning message. ​ An alternative approach to computing the message is to multiply in all of the messages and then divide the resulting factor by returning message. ​
  
-$\delta_{i \overrightarrow ​j} = \dfrac{\sum_{C_i - S_{i,j}} \beta_i(C_i)}{ \delta_{j \overrightarrow ​i}}   $+$\delta_{i \rightarrow ​j} = \dfrac{\sum_{C_i - S_{i,j}} \beta_i(C_i)}{ \delta_{j \rightarrow ​i}}   $
  
  
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