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Old 10-02-2014, 09:17 PM
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magdon magdon is offline
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Join Date: Aug 2009
Location: Troy, NY, USA.
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Default Re: Page 63 and excercise 2.8

\overline{g}(\textbf{x}) \approx \frac{1}{K} \sum\limits_{k = 1}^{K} g_k(\textbf{x}) because \overline{g}(\textbf{x}) is defined as an expectation with respect to data sets of g(x). The average over data sets approximates this expectation.

Yes, \overline{g}(\textbf{x}) is not a valid hypothesis: it may not be in your hypothesis set; it may not even be binary. It is never used as a classifier. It is just used to represent "what would happen on average after learning", and this abstract function plays a role in defining the bias in the bias variance decomposition.

Quote:
Originally Posted by Newbrict View Post
I think \overline{g}(\textbf{x}) \approx \frac{1}{K} \sum\limits_{k = 1}^{K} g_k(\textbf{x}) because it's computed over a finite set of points, whereas the actual value for \overline{g}(\textbf{x}) is an exact solution
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