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-   -   Why would variance be non-zero? (http://book.caltech.edu/bookforum/showthread.php?t=936)

 samirbajaj 08-01-2012 05:41 PM

Why would variance be non-zero?

In question 6 on the homework, we are asked to compute the variance across all data sets.

If we are sampling uniformly from the interval [-1, 1] for the calculation of g_bar, as well as for each data set (g_d), why would the variance be anything but a very small quantity? In the general case, when the data sets are not drawn from a uniform distribution, a non-zero variance makes sense, but if there is sufficient overlap in the data sets, it makes intuitive sense that the variance should be close to zero.

I ask this because my simulation results support the above (potentially flawed) theory.

Please answer the question in general terms -- I don't care about the homework answer -- I was merely using that as an example.

Thanks for any input.

-Samir

 yaser 08-01-2012 07:32 PM

Re: Why would variance be non-zero?

Quote:
 Originally Posted by samirbajaj (Post 3781) If we are sampling uniformly from the interval [-1, 1] for the calculation of g_bar, as well as for each data set (g_d), why would the variance be anything but a very small quantity? In the general case, when the data sets are not drawn from a uniform distribution, a non-zero variance makes sense, but if there is sufficient overlap in the data sets, it makes intuitive sense that the variance should be close to zero.
is the average of over different data sets . You will get different 's when you pick different 's, since the final hypothesis depends on the data set used for training. Therefore, there will be a variance that measures how different these 's are around their expected value (which does not depend on as gets integrated out in the calculation of ).

This argument holds for any probability distribution, uniform or not, that is used to generate the different 's.

 samirbajaj 08-02-2012 09:14 AM

Re: Why would variance be non-zero?

Thank you ... now that you explain it that way, it makes perfect sense. (Not sure what I was thinking...)

-Samir

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