Dear Cher Robert,
Hi et salut.
I have done work on (generalised) Bayesian (belief) networks which permit
a mix of both continuous (numeric) and discrete (symbolic, categorical)
variables. This work also permits a variable (node) to be a decision
tree function of its ancestral variables (nodes).
The work was done no later than 2003 and then published in the following
two papers (Comley and Dowe, 2003) and (Comley and Dowe, MIT Press, 2005):
@inproceedings{ComleyDowe2003,
AUTHOR ="Comley, Joshua W. and David L. Dowe",
TITLE = "Generalised {B}ayesian Networks and Asymmetric Languages",
YEAR = "2003",
Booktitle="Proc. Hawaii International Conference on Statistics
and Related Fields",
MONTH="5-8 June",
}
www.csse.monash.edu.au/~dld/David.Dowe.publications.html#ComleyDowe2003
and
@INPROCEEDINGS{ComleyDowe2005,
AUTHOR={Joshua W. Comley and David L. Dowe},
TITLE={Minimum Message Length and Generalized {B}ayesian Nets with
Asymmetric Languages},
BOOKTITLE={Advances in Minimum Description Length: Theory and
Applications},
YEAR={2005},
EDITOR={P. Gr\"unwald and M. A. Pitt and I. J. Myung},
MONTH= {April},
PAGES= {265-294},
PUBLISHER={M.I.T. Press},
ORGANIZATION={},
note={Chapter 11, ISBN 0-262-07262-9.
Final camera-ready copy submitted in October 2003},
}
www.csse.monash.edu.au/~dld/David.Dowe.publications.html#ComleyDowe2005
The work uses the Minimum Message Length (MML) principle, which dates
back to Wallace and Boulton (1968). Other good reading on MML is the
Computer Journal's most downloaded article:
Wallace, C.S. and D.L. Dowe (1999a), "Minimum Message Length and
Kolmogorov Complexity", Computer Journal, Vol. 42, No. 4, pp270-283
These and other references are in the above two Comley and Dowe papers.
When Josh Comley and I set out to do the above work, I wanted to move
in the direction of being as general as possible. Indeed, the relation
referred to in Wallace and Dowe (1999a) immediately above between MML
and Kolmogorov complexity - and the expressibility of a (Universal)
Turing Machine - suggested that this was a good (the "right"?)
framework to do this in. (And, yes, I agree about the effects that
generality tends to have on efficiency.)
In case you're interested even further, for the best read on MML,
please see the MML book by Chris Wallace himself:
Wallace, C.S. (2005), Statistical and Inductive Inference by Minimum
Message Length, Springer (Series: Information Science and Statistics),
2005, XVI, 432 pp., 22 illus., Hardcover, ISBN: 0-387-23795-X
www.csse.monash.edu.au/~dld/CSWallacePublications/index.html#CSWallaceMMLBook
I hope that feedback helps.
Best wishes and yours sincerely,
David.
On Sun, Jun 04, 2006 at 05:58:03PM -0600, Robert Dodier wrote:
> Hello,
>
> I wonder if someone can comment on the status of inference in belief
> networks in which some probabilities have numerical values while others
> have symbolic values, or values given by symbolic expressions.
>
> I am aware of some work to allow conditional distributions in discrete
> or discrete + Gaussian to be symbolic as well as numerical.
> I recently did a web search and searched the UAI mailing list archives
> but came up empty handed.
>
> My own interest in this is to construct belief networks in which
> conditional distributions can be specified by name or by an
> expression telling the pdf or cdf, and for which some parameters
> might be specified by symbols or symbolic expressions.
> Then posterior distributions, in general, can also be symbolic expressions.
> The idea here is to compute posterior distributions via a computer
> algebra system (by formulating and evaluating integrals as needed).
>
> For well-known classes of distributions, there are much more efficient
> solutions. I'm looking for greater generality, at the expense of efficiency.
>
> Any comments will be much appreciated.
>
> best,
> Robert Dodier
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> uai@ENGR.ORST.EDU
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