Hello Mohamed, Denver, et al.
These are all very interesting methods for getting the joint probability of
a small set of variables. Another method is the push operation that
effectively moves variables into parent cliques (i.e., toward the root) and
separators until the desired collection of variables are members of the same
clique.
However, I wonder if this discussion misses the mark of the original query,
which is in the context of training networks to data. If the data set is
complete (i.e., there are no hidden nodes ) then it seems the joint can be
calculated very efficiently by multiplying the appropriate entries in each
network node's cp-table. No need for any solution algorithm or join tree
here.
If the context is learning, and only one or two nodes are missing data,
what, then, is the most efficient way to obtain the joint probability? If
only one node is hidden, and the network is discrete, one can sum this
product over each of the possible values of the hidden node. Furthermore,
the calculation can be effectively restricted to the Markov neighborhood of
the hidden node. This seems to turn the approach around, to trying to find a
structure that contains the nodes that are missing data rather than one that
contains the vast majority of nodes that have data.
But I am still a little puzzled by the meaning of the original query:
> >> > 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.
> >> >
Mohamed:
Is this a question as to where the priors over network parameter values come
from?
Is the question related to how to calculate the prior probabilities of the
newly trained parameters
from the parameter priors?
It seems the discussion has been more about the likelihood of the data given
the new parameters rather than the parameter priors.
Bob
- ----- Original Message -----
From: Rina Dechter <dechter@ramat-aviv.ICS.UCI.EDU>
To: <uai@CS.ORST.EDU>
Sent: Thursday, March 30, 2000 10:55 PM
Subject: Re: Calculating joint over arbitrary sets of variables
> 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
> >
>
------- End of Forwarded Message
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