Posted by Ben Perry on February 19, 2001 at 08:30:39:
In Reply to: Re: LS Algorithm - which Lambda message to use? posted by Haipeng Guo on February 19, 2001 at 01:24:23:
Take a look at definition 7.2, page 253 in the neopolitan book - it defines S as the intersection of itself with all of its parents / grandparents. Either I'm interpreting that wrong, or else child nodes can have nodes in S that are not in its direct parent as long as the nodes are somewhere upstream.
-Ben
: I think your assumption is not correct. A child node CANNOT have nodes in S that are NOT in its direct parents' clique.
: I'm not sure how the child-parent relationships are computed in your program after the order of these cliques are determined, but I guess there may be something wrong with that parents-finding process. Please take a look at Definition 3.22 at page 102 in Neapolitan's book and the following example.
: Also please look at Step D and E on page 280.
: In your example problem, S5 is {e, l} so its parent should be C3 instead of C4. Because S5 is a subset of C3 instead of C4. According to the difinition, C3 should be its parent.
: -hpguo
: : 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.