Confactor Splitting |

If we have a confactor

we can replace it by the result of splitting it on a non-eliminated variable

<b ,t>

If

<b &Y=v_{1},t>... <b &Y=v_{k},t>

where

<b &Y=v_{1},set(t,Y=v_{1})>... <b &Y=v_{k},set(t,Y=v_{k})>

**Example.**
*
Splitting the first confactor for P(E|A,B,C,D) in Figure
* on Y gives two confactors:
*

a &y,

B E Value true true 0.55 true false 0.45 false true 0.3 false false 0.7 a & `~`

y,

B E Value true true 0.55 true false 0.45 false true 0.3 false false 0.7

**Example.**
*
Splitting the first confactor for P(B|Y,Z) in Figure
* on A gives two confactors:
*

a &y,

B Z Value true true 0.77 true false 0.17 false true 0.23 false false 0.83 `~`

a &y,

B Z Value true true 0.77 true false 0.17 false true 0.23 false false 0.83

David Poole and Nevin Lianwen Zhang,Exploiting Contextual Independence In Probabilistic Inference, Journal of Artificial Intelligence Research, 18, 2003, 263-313.

Confactor Splitting |