LFD Book Forum  

Go Back   LFD Book Forum > Book Feedback - Learning From Data > Chapter 2 - Training versus Testing

Thread Tools Display Modes
Prev Previous Post   Next Post Next
Old 11-11-2019, 05:19 AM
joseqft joseqft is offline
Junior Member
Join Date: Dec 2015
Posts: 1
Default Re: Problem 2.14(c)

I´ve 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 View Post
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.
Reply With Quote

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off

Forum Jump

All times are GMT -7. The time now is 01:41 PM.

Powered by vBulletin® Version 3.8.3
Copyright ©2000 - 2022, 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.