LFD Book Forum - Q16 and Q17 clarification

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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?

Re: Q17 and Q18 clarification

Quote:

Originally Posted by Elroch (Post 11111)

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.

Re: Q17 and Q18 clarification

Quote:

Originally Posted by jforbes (Post 11117)

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).

Re: Q17 and Q18 clarification

Quote:

Originally Posted by Elroch (Post 11118)

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.