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Michael Zedeler science forum beginner
Joined: 29 Nov 2005
Posts: 17

Posted: Sat May 06, 2006 7:15 pm Post subject:
Conformal Predictors: help wrt definition discrepancy



Hi everybody.
I have a question regarding the definition of Conformal Predictors as
defined by Vovk, Gammerman and Schafer. I am supposed to prepare a
presentation of Support Vector Machines and general machine learning as
described in the book "Algorithmic Learning in a Random World" at an
undergraduate course this coming monday.
First I'll describe the setting.
It is said that for a bag of examples
z = ((z_1, z_2, ... z_n))
Each z_i has a corresponding nonconformity score using the nonconformity
measure A as follows:
alpha_i = A( ((z_1, z_2, ..., z_n)), z_i)
To each nonconformity score a_i exists a pvalue given by
{j = 1, 2, ..., n: \alpha_j => alpha_i / n
This pvalue indicates the degree of conformity. The closer to 1 (from
below), the more conforming and the closer to 0, the more nonconforming.
No problems so far. (Hope you are still with me.)
How do I now define a conformal predictor as it is done normally? In the
book, they write that a confomal predictor has to include enough labels
from the label space, so that the pvalue is above the wanted
significance level. But it seems as if there is a discrepancy here,
because including more than one label from he label space, does not
increase the corresponding pvalue.
This means that the only option is selecting a single label that
maximizes the pvalue, but it doesn't seem to correspond the the theory
that follows, where is is emphasized that conformal predictors will
return multiple labels.
So which is right: that the only way of maximizing the pvalue is
selecting the best fitting label, or by selecting multiple labels and
somehow computing a different nonconformity score?
If you have the book, look at page 2526.
I find the book very fascinating, but it is very terse. They have a few
pages dedicated to Support Vector Machines. A subject that can easilly
take up many volumes.
Any answers will be greatly appreciated.
Regards,
Michael.

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Phil Sherrod science forum beginner
Joined: 08 Jun 2005
Posts: 37

Posted: Sat May 06, 2006 9:09 pm Post subject:
Re: Conformal Predictors: help wrt definition discrepancy



On 6May2006, Michael Zedeler <michael@zedeler.dk> wrote:
Quote:  I have a question regarding the definition of Conformal Predictors as
defined by Vovk, Gammerman and Schafer. I am supposed to prepare a
presentation of Support Vector Machines and general machine learning as
described in the book "Algorithmic Learning in a Random World" at an
undergraduate course this coming Monday.

Michael,
I'm not sure this is an exact answer for your question, but you can find a good
introduction to SVM with some good pictures at http://www.dtreg.com/svm.htm
You may be able to use the material and pictures in your presentation.

Phil Sherrod
(phil.sherrod 'at' sandh.com)
http://www.dtreg.com (decision tree and SVM modeling)
http://www.nlreg.com (nonlinear regression) 

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