Cross validation estimate

[ntvy95]

On the page 147, the book states:

In this case, the cross validation estimate will on average be an upper estimate for the out-of-sample error

My question is: Is this a leap of faith (due to "The fact that more training data lead to a better final hypothesis has been extensively verified empiricaly, although it is challenging to prove theoretically" on page 141) or is it proved?

And also by "challenging to prove", does it mean that no one has proved it yet or is it just too complicated to present in the book?

Thank you very much.

(Anyway, I've just noticed that the dot "." before the sentence I quoted on the page 141 was not properly put.)

[magdon]

It need not be true in general and it is challenging to describe simple conditions for which one can prove it to be true.

Originally Posted by ntvy95

On the page 147, the book states:



My question is: Is this a leap of faith (due to "The fact that more training data lead to a better final hypothesis has been extensively verified empiricaly, although it is challenging to prove theoretically" on page 141) or is it proved?

And also by "challenging to prove", does it mean that no one has proved it yet or is it just too complicated to present in the book?

Thank you very much.

(Anyway, I've just noticed that the dot "." before the sentence I quoted on the page 141 was not properly put.)

[ntvy95]

Originally Posted by magdon

It need not be true in general and it is challenging to describe simple conditions for which one can prove it to be true.

Thank you very much!