Dear Denver and Bruce,
When you construct join trees, include the subset for which you
desire the joint for. (I have in mind here a method for constructing
join tree starting with subsets for which you have potentials and
subsets for which you desire marginals and then stringing these in a
join tree using variable elimination). Once you have such a join
tree, one can use any known method such as Hugin, Shenoy-Shafer, SPI,
etc. Hong Xu has published a paper on precisely this problem in
Artificial Intelligence Journal (I don't have the exact reference)
using the Shenoy-Shafer architecture.
The same technique should also work for an arbitrary collection of
subsets. Of course, as Bruce says, it is not clear whether you should
do one propagation for all subsets (in one join tree) or in several
different join trees. Seems like a combinatorial (hard) problem.
-- Prakash
--
Prakash P. Shenoy
Ronald G. Harper Distinguished Professor of Artificial Intelligence
University of Kansas Business School, Summerfield Hall, Lawrence, KS 66045-2003
TEL: (785) 864-7551, FAX: (785) 864-5328
EMAIL: <[EMAIL PROTECTED]> WWW: <http://lark.cc.ukans.edu/~pshenoy>
FTP: <ftp://ftp.bschool.ukans.edu/home/pshenoy/>
