LFD Book Forum  

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

Reply
 
Thread Tools Display Modes
  #1  
Old 10-12-2015, 03:18 PM
sixdegrees sixdegrees is offline
Junior Member
 
Join Date: Oct 2015
Posts: 1
Default Problem 2.3c

I am having a bit of trouble with problem 2.3c (page 69). I have read some posts about it, including an exercise of the online course in which positive circles are treated (which I suppose is the 2D dimension of this problem).

I understand that I can transform this R^d problem into an R problem by doing in .

Thus, it turns into an equivalent case to positive intervals. However, I wonder if the growth function should change depending on the number of dimensions...

It is confusing for me to define the +1 region depending on x_1, x_2, ..., x_d. Why do we need d points in R^d? Does this mean that the binomial coefficient of the growth function depends on 'd' and not on 'N'? Does the break point change respect to positive intervals?

It would be great if you could clarify my doubts.

Thanks in advance.
Reply With Quote
  #2  
Old 10-13-2015, 12:57 PM
magdon's Avatar
magdon magdon is offline
RPI
 
Join Date: Aug 2009
Location: Troy, NY, USA.
Posts: 592
Default Re: Problem 2.3c

Yes, this problem can be reduced to positive intervals for the space [0,Inf) by the transformation you mentioned. This also explains why M(n) does not depend on d.

Quote:
Originally Posted by sixdegrees View Post
I am having a bit of trouble with problem 2.3c (page 69). I have read some posts about it, including an exercise of the online course in which positive circles are treated (which I suppose is the 2D dimension of this problem).

I understand that I can transform this R^d problem into an R problem by doing in .

Thus, it turns into an equivalent case to positive intervals. However, I wonder if the growth function should change depending on the number of dimensions...

It is confusing for me to define the +1 region depending on x_1, x_2, ..., x_d. Why do we need d points in R^d? Does this mean that the binomial coefficient of the growth function depends on 'd' and not on 'N'? Does the break point change respect to positive intervals?

It would be great if you could clarify my doubts.

Thanks in advance.
__________________
Have faith in probability
Reply With Quote
Reply

Tags
2.3c, concenctric spheres, concentric, positive intervals, spheres

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 03:50 PM.


Powered by vBulletin® Version 3.8.3
Copyright ©2000 - 2017, 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.