Denver:
Here's a simple idea. Put a latent or hidden node in between the disease
nodes and the symptoms. Use a naive Bayes classifier structure from the
hidden node to the feature variables. Then use structured learning to find
the number of states in the hidden node. Train the network using EM with n
states in the hidden node. Then search over n using a criterion that
penalizes the number of parameters in the network. If the diseases are
binary nodes, and there are m of them, then n should range between 2 and 2^m
. At 2^m you have the equivalent of MPE: each state of C corresponds to one
combination of the diseases.
D1 S1
\ /
\ /
D2 ---- C ------- S2
/ \
/ \
D3 S3
Arcs are directed from Di to C and C to Si. For binary D's and S's the
number of parameters is n*(2^m + q) where q = the number of features.
An alternative is to run all the arcs out from C and train as an
unsupervised naive Bayes classifier, again searching for the number of
states in C. Now the number of parameters is n*(m+q).
Apply MPE as JD suggests one the classifier is trained.
Bob Welch
- ----- Original Message -----
From: "J.D. Park" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Friday, August 09, 2002 7:45 PM
Subject: Re: [UAI] classific. w/ multiple related class nodes
> Computing the most likely configuration of a set of variables, at least
> in the BN community, is known as computing the Maximum a Posteriori
> hypothesis, or MAP. If all of the nodes in your model are either
> observed or ones you want to maximize over, then it is a special case of
> MAP often called Most Probable Explanation, or MPE. Assuming that you
> have a model already, there are a variety of inference algorithms that
> will solve it for you. A web search on MPE turns up a number of papers
> on it. If instead, you are attacking it from a learning perspective,
> trying to generate an especially good model for producing accurate MAP
> configurations relative to some training data, I am not aware of any
> algorithms developed specifically for that purpose.
> Hope that helps,
> J.D. Park
>
> On Friday, August 9, 2002, at 12:39 PM, DENVER H DASH wrote:
>
> > Hi all,
> >
> > I'm looking for references, or even some vocabulary, addressing
> > or describing the problem of classification with multiple, non-disjoint
> > and possibly related class variables.
> >
> > For example, in a medical diagnosis BN classifier with several possible
> > disease nodes: the disease nodes are not mutually exclusive, so the
> > classification problem is to decide which joint configuration of class
> > variable states is most likely, rather than which state of a single
> > class
> > variable is most likely.
> >
> > I'd be grateful for any pointers to this problem.
> >
> > Cheers,
> > Denver.
> >
>
