On 2/11/2011 11:32 AM, Rich Neapolitan wrote:
Once again, I am going against the grain and submitting a post that is
not a job ad or a conference announcement. I hope no one takes offense.
My question concerns the noisy-OR model. The traditional way to assess a
parameter value for a given cause is to use the data items that only
have that cause present. However, if there are many causes and limited
data, there will be few such data items. I want an approximation method
that deals with this problem. A quick Google search did not reveal any
previous work in this area. I have a few ideas, but I thought I would
first ask if anyone knows of anything that has already been done in this
area.
Rich,
Please look at a review paper "Canonical probabilistic models for
knowledge engineering" co-authored by Javier Diez and myself:
http://www.ia.uned.es/~fjdiez/papers/canonical.html
Of importance in this task are two ways of specifying the parameters of
the Noisy-OR model, one due to Max Henrion and the other due to Javier
Diez (references in our review paper). In learning from data, Max's
specification seems to be generally more convenient.
An IJAR paper co-authored by Agnieszka Onisko and myself,
Agnieszka Onisko, Marek J. Druzdzel and Hanna Wasyluk. Learning Bayesian
network parameters from small data sets: Application of Noisy-OR gates.
International Journal of Approximate Reasoning, 27(2):165-182, 2001.
shows a simple way of doing what you want. We have done more work on
this, although we have not published it yet.
Also, there is an implicit another way of doing this, embedded in GeNIe
(http://genie.sis.pitt.edu/) -- you can fit a Noisy-OR/MAX distribution
to an existing CPT. So, learning a CPT and then fitting a Noisy-OR/MAX
is a possible approach. The fitting algorithm is described in a paper
co-authored by Adam Zagorecki and myself:
Adam Zagorecki and Marek J. Druzdzel. Knowledge engineering for Bayesian
networks: How common are noisy-MAX distributions in practice?. In
Proceedings of the Seventeenth European Conference on Artificial
Intelligence (ECAI-06), G. Brewka, S. Coradeschi, A. Perini & P.
Traverso (eds.), pages 482-489, Amsterdam: IOS Press, 2006.
Adam's doctoral dissertation contains more details.
I hope this helps.
Cheers,
Marek
----------------------------------------------------------------------
Marek J. Druzdzel http://www.pitt.edu/~druzdzel
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