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yaser · #2 05-05-2013, 09:07 PM

Quote:

Originally Posted by marek

I am struggling to understand how to calculate $E_{out}$ in this question. I have two competing theories, which I will describe below. Any help is greatly appreciated.

Once the algorithm terminates, I have $w^{(t)}$ . I now generate a new set of data points $\{X_i\}_{i=1}^M$ . Using my original target function to generate the corresponding

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Case 1. Just use the same cross entropy error calculation but on this new data set.

$E_{out} = \frac{1}{M} \sum_{i=1}^M \ln (1+e^{-Y_i w^\top X_i})$

The above approach is correct. The problem specifies the cross entropy error measure, so $E_{\rm out} = {\rm E} [ \ln (1+e^{-y{\bf w}^\top {\bf x}})]$ , where the expectation is w.r.t. both ${\bf x},y$ . The above formula estimates that through a random sample.