Re: Calculating joint over arbitrary sets of variables

From: Rina Dechter (dechter@ramat-aviv.ICS.UCI.EDU)
Date: Thu Mar 30 2000 - 21:55:52 PST

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    Hi,
    You can just use bucket-elimination algorithm where the subset
    of variables queried are processed last (initiate the ordering).
    The complexity will be exponential in the induced-width
    of the moral graph computed along this restricted
    ordering.

    ------Rina
    >Hi, this is a repost of a previous thread (BDe scoring metric). I thought I
    >would repost it under this title to see if it gets a better response.
    >Basically I'm looking for an efficient way to calculate the joint of an
    >arbitrary subset of nodes in a Bayes net. Below is one algorithm I
    >proposed, but it's not terribly efficient.
    >
    >Thanks,
    >Denver.
    >
    >- ----- Original Message -----
    >From: "Denver Dash" <ddash@isp.pitt.edu>
    >To: <uai@CS.ORST.EDU>
    >Sent: Thursday, March 23, 2000 5:23 PM
    >Subject: Re: [UAI] BDe scoring metric
    >
    >
    >> Basically you need to calculate the joint over an arbitrary subset of
    >> variables: P(V1,V2,...Vm) where m<n (the total number of variables).
    >>
    >> One way to do this is to do the following:
    >>
    >> Make use of the fact that P(V1,V2,...,Vm) is equal to
    >> P(V1)P(V2|V1)P(V3|V1,V2)...P(Vm|V1,...,Vn-1).
    >>
    >> This suggests the following algorithm to calculate the joint of a subset S
    >> of nodes:
    >>
    >> Evidence_Set = {};
    >> jointProb = 1;
    >>
    >> For each node V in S do:
    >> Update beliefs in network given Evidence_Set.
    >> query node V to get P(V|Evidence_Set).
    >> jointProb = jointProb * P(V|Evidence_Set)
    >> Evidence_Set += V
    >>
    >> Of course if the nodes are in the same clique then you can find a more
    >> efficient way to calculate their joint (marginalize the potentials over
    >the
    >> non-included variables), but in general this won't be the case.
    >>
    >> I would also be interested if anybody knows of a more efficient way to do
    >> this calculation in general.
    >>
    >> Cheers,
    >> Denver.
    >> --
    >> Denver Dash http://www.sis.pitt.edu/~ddash
    >>
    >> ----- Original Message -----
    >> From: "Mohamed Bendou" <mohamed@esiea-ouest.fr>
    >> To: <uai@CS.ORST.EDU>
    >> Sent: Thursday, March 23, 2000 12:58 PM
    >> Subject: [UAI] BDe scoring metric
    >>
    >>
    >> > Hi,
    >> > I try to program the BDe scoring metric for learning bayesian networks.
    >> > Could you indicate me reference to the algorithmic aspects of
    >> > calculating priors on parameters?
    >> > I do not understand how i can calculate efficiently the prior joint
    >> > probabilities
    >> > from the prior network.
    >> >
    > > Thank you.
    >> >
    >> >
    >> > Mohamed BENDOU
    >> >
    >> >
    >> > --
    >> > Mohamed BENDOU
    >> >
    >> >
    >>
    >
    >
    >------- End of Forwarded Message
    >



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