As we have seen in the previous section, one kind of approach for exploiting causal independencies is to use them to transform BNs. Thereafter, any inference algorithms, including CTP or VE , can be used for inference.
We found the coupling of the network transformation techniques and CTP was not able to carry out inference in the two CPCS networks used in our experiments. The computer ran out memory when constructing clique trees for the transformed networks. As will be reported in the next subsection, however, the combination of the network transformation techniques and VE was able to answer many queries.
This paper has proposed a new method of exploiting causal independencies. We have observed that causal independencies lead to a factorization of a joint probability that is of finer-grain than the factorization entailed by conditional independencies alone. One can extend any inference algorithms, including CTP and VE , to exploit this finer-grain factorization. This paper has extended VE and obtained an algorithm called VE1 . VE1 was able to answer almost all queries in the two CPCS networks. We conjecture, however, that an extension of CTP would not be able to carry out inference with the two CPCS networks at all. Because the resources that VE1 takes to answer any query in a BN can be no more than those an extension of CTP would take to construct a clique tree for the BN and there are, as will be seen in the next subsection, queries in the two CPCS networks that VE1 was not able to answer.
In summary, CTP based approaches are not or would not be able to deal with the two CPCS networks, while VE -based approaches can (to different extents).