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Conformal Predictors: help wrt definition discrepancy
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Michael Zedeler
science forum beginner


Joined: 29 Nov 2005
Posts: 17

PostPosted: Sat May 06, 2006 7:15 pm    Post subject: Conformal Predictors: help wrt definition discrepancy Reply with quote

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 p-value given by

|{j = 1, 2, ..., n: \alpha_j => alpha_i| / n

This p-value 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 p-value 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 p-value.

This means that the only option is selecting a single label that
maximizes the p-value, 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 p-value 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 25-26.

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.
--
Which is more dangerous? TV guided missiles or TV guided families?
Visit my home page at http://michael.zedeler.dk/
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Phil Sherrod
science forum beginner


Joined: 08 Jun 2005
Posts: 37

PostPosted: Sat May 06, 2006 9:09 pm    Post subject: Re: Conformal Predictors: help wrt definition discrepancy Reply with quote

On 6-May-2006, 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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