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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