Exact inference methods, based on strong junction trees, were worked out by Lauritzen et al, but can lead to v large cliques. Indeed, Lerner01 proves that inference is NP-hard even in tree-structured hybrid nets. (http://robotics.Stanford.EDU/~uri/Papers/)
Hence one needs to resort to approximations. One heuristic is to violate the *strong* jtree requirement: this amounts to doing moment matching (weak marginalization) in both the forwards and backwards passes over the tree. A more aggressive heuristic is to violate the *jtree* requirement: this amounts to doing expectation propagation (see http://www.stat.cmu.edu/~minka/papers/ep/) Of course, one can always use (Rao-Blackwellised) sampling, which is simple to implement and has well-understood theoretical properties. An orthogonal issue is that the Lauritzen method forbids discrete nodes from having continious parents, which is useful for modelling threshold behavior. I applied a variational approximation due to Jaakkola to avoid this problem; Lerner (UAI 01) combined Lauritzen's algorithm and numerical integration. Both solutions are rather complicated, however. HTH, Kevin - ----- Original Message ----- From: "Adam Sosnowski" <[EMAIL PROTECTED]> Date: Wednesday, August 28, 2002 4:29 pm Subject: Re: [UAI] BN with continous and disctet variables > > > adam: could you put the replies you got onto a web page > > and email the url to the list? I suspect a lot of people > > (myself included) would be interested. --sam > > > > > > Sam Roweis -- Department of Computer Science -- University > of Toronto > > www.cs.toronto.edu/~roweis roweis [at] cs [dot] > toronto [dot] edu > > > No problem, here is the url: > http://strony.wp.pl/wp/adsosn/mails.htm > > Adam > > -------------------------------------------------------------------- > --- > Co m�wi Twoja poczta g�osowa? Sprawd�! < http://powitania.wp.pl > >
