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-   -   Calculating The "Average" Function Of Xn (http://book.caltech.edu/bookforum/showthread.php?t=950)

munchkin 08-05-2012 11:41 AM

Calculating The "Average" Function Of Xn
 
Page 63 seems to be saying this:

For each data set, evaluate the hypothesis for that data and save it somewhere. When all of the data has been processed take each data point and calculate the "average" value of that data point evaluated against each of the previously generated hypotheses. That average value can be used to calculate the variance of the data set.

So this is just a straightforward averaging calculation, is it not? I'm having some difficulty duplicating the variance values shown in the examples from the book and suspect that this calculation may be the source of the problem.

Thanks for your attention.

yaser 08-05-2012 02:28 PM

Re: Calculating The "Average" Function Of Xn
 
Quote:

Originally Posted by munchkin (Post 3811)
For each data set, evaluate the hypothesis for that data and save it somewhere. When all of the data has been processed take each data point and calculate the "average" value of that data point evaluated against each of the previously generated hypotheses. That average value can be used to calculate the variance of the data set.

Just to clarify. After you have calculated the various hypotheses based on different data sets, you evaluate these hypotheses on a generic point {\bf x} (not necessarily belonging to any data set used for training). The average value you get will be \bar g ({\bf x}) and the variance in the values you get will be {\bf var}({\bf x}). The expected value of {\bf var}({\bf x}) with respect to {\bf x} (based on the uniform probability of generating {\bf x}) is the variance {\bf var}. Is this what you have calculated?

munchkin 08-05-2012 04:44 PM

Re: Calculating The "Average" Function Of Xn
 
Thanks for your quick reply. I have managed to duplicate the variance result for hypothesis zero of example 2.8. The error had nothing to do with averaging. I don't use a generic x but simply calculate the average of all of the g's generated by the test data sets. This averaged g is evaluated at each data point where comparison with g(x) is required. It seems to work for the constant value case.

The book says that the average g is calculated for "a particular x" and is interpreted as the expected value of the random variable gbar(X). Is this particular x value the "generic" value?

yaser 08-05-2012 09:05 PM

Re: Calculating The "Average" Function Of Xn
 
Quote:

Originally Posted by munchkin (Post 3816)
The book says that the average g is calculated for "a particular x" and is interpreted as the expected value of the random variable gbar(X). Is this particular x value the "generic" value?

Correct. This is just to simplify the concept, but your approach of getting the whole \bar g at once is certainly valid.


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