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-   -   Q16 and Q17 clarification (http://book.caltech.edu/bookforum/showthread.php?t=4346)

Elroch 06-11-2013 07:21 AM

Q16 and Q17 clarification
 
In these two questions there are the independent possibilities of E_{in} rising falling or staying the same and the same for E_{out}. In the latter case, while for the two inequalities the meaning is clear and based (with high confidence) on an adequate test sample, what the precise meaning would be for equality is not clear.

In any case, the options are not complete (there are 5 of 9), so presumably what is wanted is the greatest from those offered, regardless of whether it is actually the most frequent possibility?

In any case, could you clarify the precise meaning of the fifth option?

jforbes 06-11-2013 11:34 AM

Re: Q17 and Q18 clarification
 
Quote:

Originally Posted by Elroch (Post 11111)
In these two questions there are the independent possibilities of E_{in} rising falling or staying the same and the same for E_{out}. In the latter case, while for the two inequalities the meaning is clear and based (with high confidence) on an adequate test sample, what the precise meaning would be for equality is not clear.

In any case, the options are not complete (there are 5 of 9), so presumably what is wanted is the greatest from those offered, regardless of whether it is actually the most frequent possibility?

In any case, could you clarify the precise meaning of the fifth option?

I used the same test set to evaluate the out of sample error for the alternatives, so it was in principle quite possible to get the same E_{out}. I'm not sure if this was the appropriate approach.

In principle though, what you're doing with your test set is you're approximating the true value of E_{out}, which you only approach in the limit of an infinite test set, in which case the probability that you get exactly the same E_{out} should be vanishingly small unless your hypotheses were the same exact function, which won't happen in our situation.

Elroch 06-11-2013 11:59 AM

Re: Q17 and Q18 clarification
 
Quote:

Originally Posted by jforbes (Post 11117)
I used the same test set to evaluate the out of sample error for the alternatives, so it was in principle quite possible to get the same E_{out}. I'm not sure if this was the appropriate approach.

In principle though, what you're doing with your test set is you're approximating the true value of E_{out}, which you only approach in the limit of an infinite test set, in which case the probability that you get exactly the same E_{out} should be vanishingly small unless your hypotheses were the same exact function, which won't happen in our situation.

I realise that, and was using a large test set, so the situation did not arise. What I did have on one question was a lot of unchanged E_{in} and different E_{out}. As I result, I was uncomfortable with my answer (although it was correct).

jforbes 06-11-2013 01:39 PM

Re: Q17 and Q18 clarification
 
Quote:

Originally Posted by Elroch (Post 11118)
I realise that, and was using a large test set, so the situation did not arise. What I did have on one question was a lot of unchanged E_{in} and different E_{out}. As I result, I was uncomfortable with my answer (although it was correct).

Ah, good point. I didn't check all 9 conditions, just the 5 given. There was a clear winner every time, even with a not-ridiculously-large test set, so I didn't bother checking that scenario, which in retrospect seems like it could indeed arise frequently.


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