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 09-28-2014, 04:51 PM
cbmachine cbmachine is offline
Junior Member
 
Join Date: Sep 2014
Posts: 3
Default Page 63 and excercise 2.8

On page 63 its given that g_(x) is approximately the mean of all gk(x) for any x. Why is it an estimate and not exactly the mean?

Since g_(x) is the average for any x, then its possible for it to have non binary values for a binary classification problem. But this seems to be a bit counter intuitive to me. Can you please clarify if my understanding of g_(x) is correct
Reply With Quote
  #2  
Old 10-01-2014, 06:43 PM
Newbrict Newbrict is offline
Junior Member
 
Join Date: Sep 2014
Posts: 1
Default Re: Page 63 and excercise 2.8

I think \overline{g}(\textbf{x}) \approx \frac{1}{K} \sum\limits_{k = 1}^{K} g_k(\textbf{x}) because it's computed over a finite set of points, whereas the actual value for \overline{g}(\textbf{x}) is an exact solution
Reply With Quote
  #3  
Old 10-02-2014, 09:17 PM
magdon's Avatar
magdon magdon is offline
RPI
 
Join Date: Aug 2009
Location: Troy, NY, USA.
Posts: 595
Default Re: Page 63 and excercise 2.8

\overline{g}(\textbf{x}) \approx \frac{1}{K} \sum\limits_{k = 1}^{K} g_k(\textbf{x}) because \overline{g}(\textbf{x}) is defined as an expectation with respect to data sets of g(x). The average over data sets approximates this expectation.

Yes, \overline{g}(\textbf{x}) is not a valid hypothesis: it may not be in your hypothesis set; it may not even be binary. It is never used as a classifier. It is just used to represent "what would happen on average after learning", and this abstract function plays a role in defining the bias in the bias variance decomposition.

Quote:
Originally Posted by Newbrict View Post
I think \overline{g}(\textbf{x}) \approx \frac{1}{K} \sum\limits_{k = 1}^{K} g_k(\textbf{x}) because it's computed over a finite set of points, whereas the actual value for \overline{g}(\textbf{x}) is an exact solution
__________________
Have faith in probability
Reply With Quote
Reply

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 07:45 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.