Summing Out A Variable That Appears In The TableContextual Variable EliminationMultiplying Contextual Factors

Multiplying Contextual Factors

If we have two confactors with the same context:
<b ,t1> 
<b ,t2> 
we can replace them with their product:
<b ,t1×tt2>. 
The program invariant is maintained, as any context incompatible with b isn't affected by this operation. Any context that is compatible with b, the product of the values of t1 and t2 on that context is the same as the value of t1×tt2 on that context. The completeness part of the invariant isn't affected by multiplying.
David Poole and Nevin Lianwen Zhang,Exploiting Contextual Independence In Probabilistic Inference, Journal of Artificial Intelligence Research, 18, 2003, 263-313.

Summing Out A Variable That Appears In The TableContextual Variable EliminationMultiplying Contextual Factors