Thread: Discussion of the VC proof View Single Post
#4
11-18-2012, 04:29 AM
 eakarahan Junior Member Join Date: Nov 2012 Posts: 3
Re: The VC Proof

Quote:
 Originally Posted by admin For the courageous souls who read the VC proof in the Appendix carefully, please use this subforum to post any questions or comments. In particular, we will appreciate any comments that help us and other instructors decide whether to include the formal proof in our classroom presentations, or settle for the sketch of the proof that is given in Chapter 2.
First comment about the proof in Appendix: I experienced a notation problem with P(x, y). This has two meanings. Joint probability or probability density. I would prefer another notation for density, since using one notation with two meanings is ambiguous.

For your question I would like to say: Due to the mixed mathematical background of any classroom, include the formal proof in your classroom presentations. Further, I suggest that you extract the proof from the appendix and include it in the text in Chapter 2, since I think it would be more natural that you develop VC-bound within the lecture formally.

I never like God send formulas, I like to understand the natural development of these ideas and learn how mathematicians transform these ideas into the formulas without any break. A deferred proof, break this sequence force us to remember what was referring what.

If you think the opposite, than enhance your Appendix so that the derivations are given step by step with helping explanations beyond the formulas. Current format of the proof requires the student create this sequence by her/himself. I want to know what is the natural historical development sequence of these ideas. Maybe I should refer the VC-book, Statistical Learning Theory. But, I need the help of an instructor like you, since reading a 750 pages book is infeasible; especially if you yearn for writing your first ML applications within the next 3 months.

For human being english is always better then notations, but notations are inevitable to avoid ambiguities; thus a combination of both is the ideal format. I see you try to achieve this ideal. This is good, so.

At the moment that I wrote this message, I've watched the 6. video and read the book until Chp 2, section 2.3 and I read the two pages of the proof in appendix. Until now, two thinks broke me disturbing my mind; how the Hoeffding found his from God send inequality, and how can I understand the long derivations of VC-Bound including the mathematical technicalities you mention in the book and videos. I'm still working on the second one. And try to accept Hoeffding's inequality as given (which disturbs my mind like a bug in my brain and decelerates my learning).

I know you want to show us the forest instead of dealing with the leaves of trees, but you can do this like you have done in the book between th pages 46-49 using "safe skip" blocks.

A last word, this is the first ML course that I could see the whole picture, the forest. As such this is the first successful attempt that I experienced.

Thank you all, for your effort.