Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

We now compute the messages that node V sends to its parents U and each of
its children Z1, Z2, …,Zn to update their values. Each of these two messages is
a conditional probability, given that the condition holds and the probability
given that it does not.
Now, the message from V to parent U, denoted by λv (U), is computed as
λv(U) = ∑v ∈(true, false) P(ev - |U, V = v) P(V = v | U)
= ∑v∈(true,false) P(ev - |,V= v) P (V = v |U)
= ∑ v ∈(true,false) P(V = v |U) λ (V = v)
= [P(V | U)]2 x 2 x [λ(0) λ(1)] T 2 x 1 (9.17)
Lastly, the message from V to its child Zj is given by
∏ Zj (V)
= P(V⏐eZi + )
= P(V⏐ev + , eZ1 - , eZ2 - , ……, eZi-i - , eZi+ i - ,………, eZn - )
= β ∏j≠i P(eZi - ⏐V, ev + ) P(V⏐ev + )
= β ∏j≠iP(ezi - ⏐V) P(V⏐ev + )
=β( ∏j≠iλZi (V)) ∏(V)
=β(λ(V)/ λZj(V)) ∏(V)
=β Bel (V)/ λZj(V) (9.18)
where β is a normalizing constant computed similarly as α.
The belief updating process at a given node B (in fig. 9.4) has been
illustrated based on the above expressions for computing the λ and ∏
messages. We here assumed that at each node and link of the tree (fig. 9.4) we
have one processor [7]. We call these node and link processor respectively. The
functions of the node and the link processors are described in fig. 9.6.