LFD Book Forum  

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

Reply
 
Thread Tools Display Modes
  #21  
Old 09-28-2012, 06:30 PM
rozele rozele is offline
Junior Member
 
Join Date: Sep 2012
Posts: 1
Default Exercise 2.4b

The final part of the hint in this question says:
"Now, if you choose the class of these other vectors carefully, then the classification of the dependent vector will be dictated."
The other vectors refers to the set of linearly independent vectors that make up the d+2th vector. What do you mean by class? Do you mean class of vector, (e.g., unit vector), or class based on the PLA algorithm (i.e., +1 or -1)?
Reply With Quote
  #22  
Old 09-29-2012, 07:00 AM
magdon's Avatar
magdon magdon is offline
RPI
 
Join Date: Aug 2009
Location: Troy, NY, USA.
Posts: 592
Default Re: Exercise 2.4b

Class means \pm1. (Note: there is no PLA or algorithm here; the VC dimension has only to do with the hypothesis set.)

At this point you have established that some input vector x^* is linearly dependent on the others. If you assign the class (\pm1) of the other vectors appropriately, you should be able to show that the linear dependence dictates that the class of x^* must be (say) +1. This means you cannot implement -1 with the other points having those appropriately chosen classifications, and hence this data set cannot be shattered.

This argument will apply to any data set of d+2 points, and so you cannot shatter any set of d+2 points.

Quote:
Originally Posted by rozele View Post
The final part of the hint in this question says:
"Now, if you choose the class of these other vectors carefully, then the classification of the dependent vector will be dictated."
The other vectors refers to the set of linearly independent vectors that make up the d+2th vector. What do you mean by class? Do you mean class of vector, (e.g., unit vector), or class based on the PLA algorithm (i.e., +1 or -1)?
__________________
Have faith in probability
Reply With Quote
  #23  
Old 09-29-2012, 09:44 PM
nahgnaw nahgnaw is offline
Junior Member
 
Join Date: Aug 2012
Posts: 4
Default Problem 2.24

When we design the numerical experiment, shall we randomly generate more datasets to determine g_bar(x), E_out, bias, and var?
Reply With Quote
  #24  
Old 09-30-2012, 05:16 AM
magdon's Avatar
magdon magdon is offline
RPI
 
Join Date: Aug 2009
Location: Troy, NY, USA.
Posts: 592
Default Re: Problem 2.24

Yes, when computing bias and var numerically you need to generate many data sets. For example, \bar g(\mathbf{x}) is the average function that results from learning on each of these data sets.

Quote:
Originally Posted by nahgnaw View Post
When we design the numerical experiment, shall we randomly generate more datasets to determine g_bar(x), E_out, bias, and var?
__________________
Have faith in probability
Reply With Quote
  #25  
Old 07-11-2017, 05:15 AM
RicLouRiv RicLouRiv is offline
Junior Member
 
Join Date: Jun 2017
Posts: 7
Default Re: Exercises and Problems

Professor -- in my version of the text, for 2.14.b, the inequality is:

2^l > 2Kl^{d_{VC}}.

It looks like others are using a version of the inequality that is:

2^l > Kl^{d_{VC}+1},

which I think makes the problem a little more transparent. I'm wondering if there's a typo in my version? If not, any additional hints on how to treat this version of the inequality would be helpful.
Reply With Quote
Reply

Tags
errata, growth function, perceptron

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 03:42 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.