LFD Book Forum

LFD Book Forum (http://book.caltech.edu/bookforum/index.php)
-   Chapter 2 - Training versus Testing (http://book.caltech.edu/bookforum/forumdisplay.php?f=109)
-   -   Problem 2.14(c) (http://book.caltech.edu/bookforum/showthread.php?t=1876)

joseqft 11-11-2019 05:19 AM

Re: Problem 2.14(c)
Ive been struggling with this problem too. Essentialiy we have to prove that the second expression in the min expression


is a valid \ell as explains magdon in


Originally Posted by magdon (Post 11695)
Rather than solve the inequality in (b) to get this bound, you may rather just verify that this is a bound by showing that if \ell=7(d_{VC}+K)\log_2(d_{VC}K), then the inequality in (b) is satisfied, namely 2^\ell>2K\ell^{d_{VC}}.

this means that the inequality

(d_{VC}+K)^{7(d_{VC}+K)} > 2K\left[7(d_{VC}+K)\log_2(d_{VC}K)\right]^{d_{VC}} (1)

must be satisfied.

I have been finding upper bounds to the right hand side of (1), using the following tricks

d_{VC}+K \geq d_{VC}K if d_{VC}\geq 2 (the case d_{VC}= 1 must be proved apart).

\log_2(d_{VC}K) < d_{VC}K,

7 < 2^3 \leq K^3, because K \geq 2 (this is not the seven in the exponent) and

K + 1< K^2.

Then we arrive at an expression that can be compared easily with the left hand side of (1) proving that this inequality is valid.

All times are GMT -7. The time now is 01:45 PM.

Powered by vBulletin® Version 3.8.3
Copyright ©2000 - 2019, Jelsoft Enterprises Ltd.
The contents of this forum are to be used ONLY by readers of the Learning From Data book by Yaser S. Abu-Mostafa, Malik Magdon-Ismail, and Hsuan-Tien Lin, and participants in the Learning From Data MOOC by Yaser S. Abu-Mostafa. No part of these contents is to be communicated or made accessible to ANY other person or entity.