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Old 10-01-2015, 07:32 PM
ilson ilson is offline
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Join Date: Sep 2015
Posts: 10
Default Re: Discussion of the VC proof

I was going through the proof in Appendix A and I just want to make sure that something written towards the bottom of pg. 189 is a typo.

Namely,

Quote:
Inequality (A.3) folows because the events "|E'_{in}(h^*)-E_{out}(h^*)|\leq \frac{\epsilon}{2}" and "|E_{in}(h^*)-E_{out}(h^*)|>\epsilon" (which is given) imply "|E_{in}(h)-E'_{in}(h)|>\frac{\epsilon}{2}".
should read

Quote:
Inequality (A.3) folows because the events "|E'_{in}(h^*)-E_{out}(h^*)|\leq \frac{\epsilon}{2}" and "|E_{in}(h^*)-E_{out}(h^*)|>\epsilon" (which is given) imply "|E_{in}(h^*)-E'_{in}(h^*)|>\frac{\epsilon}{2}".
I'm 99.999999999999% sure this is indeed a typo since the latter case easily follows from reverse triangle inequality and it suffices to show the inequality in (A.3) and I cannot see how one can arrive at the implication in the former case nor how the former case implies the inequality (A.3), but it would ease my mind if I can get a verification that it is a typo. Thank you in advance!
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