Posted by Ben Perry on February 18, 2001 at 15:58:22:
Assuming that it is okay to have child cliques have nodes in the S group that do not belong to the immediate parent, then how should ambiguous lambda messages be treated?
For example, clique 5 in the previous thread has nodes 'C' and 'E' in the S group. The lambda messages are L(c1, e1), L(c1, e2), L(c2, e1), and L(c2, e2). When it sends the messages back up to the parent (clique 4), the parent goes through all of its phi values and multiplies them by the corresponding lambda messages. It does this by seeing which node in the current cliqueset matches one of the lambda messages. (the key word being "one"). However, because clique 4 doesn't contain node 'E', the lambda messages are no longer on a one-to-one correspondence and thus can have two possible lambda messages (ex: c1, e1 and c1, e2 both correspond to c1). Which one (or do we sum all possible values) should we use?
Again, this is assuming that it is okay for children to have nodes in S that are NOT in its direct parent's clique.