Dear Robert:
On Fri, 6 Apr 2001 R.G.Cowell@city.ac.uk wrote:
> Several Bayes net structure learning algorithms work incrementally by
> testing the addition of a single link to a current model, seeing if
> it improves some score, such as marginal likelihood, and then
> selecting the link which increases the score the most. I remember that
> there were some papers a few years back pointing out that this
> single-link look-ahead search fails for some special situations and
> the simultaneous addition of two links should be considered instead,
> but I cannot recall any details of the papers.
>
> I would be grateful if anyone can provide references to papers which
> deal with this issue.
A paper that deals with this issue is:
David Madigan, Steen A. Andersson, Michael D. Perlman, and Chris T.
Volinsky. "Bayesian Model Averaging and Model Selection for
Markov Equivalence Classes of Acyclic Digraphs."
_Communications in Statistics (Theory and Methods)_, 25, 11 (1996), pp.
2493-2512. See in particular p.7 of the online version:
http://www.stat.washington.edu/bayes/PAPERS/dstarbma.ps. The example
given on that page shows how one cannot move from a V-structure on three
nodes to a different V structure on the same three nodes by changing only
one edge. (This seems obvious.) It is claimed on the same page that
changing one or two edges at a time overcomes this problem.
> Thanks in advance.
You are welcome.
>
> Robert Cowell
> Department of Actuarial Science and Statistics
> City University
> Northampton Square
> London EC1V 0HB
>
> tel: (44) 020 7477 - 8454
> fax (44) 020 7477 - 8838
> www: http://www.staff.city.ac.uk/~rgc
>
Marco
Marco Valtorta Associate Professor
Dept. of Computer Science and Engineering mgv@cse.sc.edu
University of South Carolina tel: (1)(803)777-4641 fax: -3767
Columbia, SC 29208, U.S.A. http://www.cse.sc.edu/~mgv/ tlx: 805038 USC
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"Probability is not about numbers. It is about the structure of reasoning."
--Glenn Shafer
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