Hi Denver,
Thanks for your reply.
My intention is the first of your interpretation.
So by that way, we can generate a random JPD along a perfect
map DAG D. That is, if a JPD can be generated by generating
a set of conditional probability distributions {P(Xi|II(Xi))}
(II(Xi) are parents of Xi in a DAG D on an ordering X1,X2,...,Xn)
such that II(Xi) is the minimum set of predecessors satisfying
P(Xi|II(Xi))=P(Xi|X1,...,Xi-1), then the DAG D is a perfect map
of the JPD. I think this saying is equivalent to your statement
in (1).
My question is, we know for a JPD, there is no guarantee that
a DAG exists to be its perfect map. I want to know what properties
make such generated JPD to have the DAG to be its perfect map?
i.e. What makes the JPD read off the DAG special from a randomly
given JPD which may not have a perfect map DAG?
Xiangdong
On Wed, 26 Sep 2001, Denver Dash wrote:
> I can think of at least two ways to interpret what you are trying to do,
> here is the answer for all three interpretations:
>
> (1) I want to generate a random JPD along with its perfect map D.
> To do this, it is sufficient to construct a random dag and randomly set the
> parameters so that no two columns in a given table are identical. The dag
> will be a perfect map to the JPD generated by the network.
>
> (2) Given a JPD I want to construct its perfect map D.
> As far as I know, the only way to do this is to query the JPD for
> independence relations along the lines of a constraint-based learning
> algorithm, for example the PC algorithm (given in the book "Causation,
> Prediction and Search", Spirtes, Glymour and Scheines), or Pearl and Verma's
> algorithm (http://citeseer.nj.nec.com/pearl91theory.html).
>
> Hope this helps,
> Denver.
> ----
> Denver Dash http://www.sis.pitt.edu/~ddash
