"Denver H. Dash" wrote:
>
> Geiger and Heckerman (I don't have the reference handy) showed that
> given some assuptions non-uniform parameter priors can be calculated
> on the fly using only a single elicited prior network and an
> equivalent sample size for the expert. This method requires you to
> use the prior network to calculate the probability P(X,Pa(X)) where
> Pa(X) are the parents of X in the network being tested (not the prior
> network). Therefore, in the prior network, the set of variables
> {X,Pa(X)} are not necessarily in the same clique.
>
Let me add a bit to this.
I worked on the EM-algorithm to learn parameters in BNs with missing
data. Now if one wish to learn the structure at the same time, it
changes along the way and then one has the above problem (on a larger
scale):
Sufficient statistics in the EM-algorithm are sums (over data cases) of
joint probs for families {X,pa(X)} in the _new_ structure, but the
expectation is to be taken wrt. the _old_ structure and the parameters
there.
One can use the push operation/variable propagation as mentioned
earlier. I thought of a similar, but more "permanent" method:
Moralize the old structure. Then add links so that families in the new
structure are also fully connected in the old structure. This will
assure that the resulting JT will contain the new families in at least
one clique. This might be easier when one has to not only consider one
prior network, but a large set of learning data. (has not been tested
though)
One can do better though: the extra links need only be added between
missing variables/nodes. (~Bob Welch's remark on one/two missing
variables.) The reason is that if some variable(s) in a family is/are
observed one only need the joint prob for the remaining family members.
(~The covariance vanishes if at least one of the "co-variables" is
observed)
So possibly one should have different networks for different patterns of
missing data.
That was the problem viewed through EM glasses. I hope it shed some new
light on the case.
Regards,
Johan Andersen
Aalborg University, Denmark
This archive was generated by hypermail 2b29 : Mon Apr 03 2000 - 15:39:25 PDT