LFD Book Forum  

Go Back   LFD Book Forum > Course Discussions > Online LFD course > Homework 2

Reply
 
Thread Tools Display Modes
  #1  
Old 07-24-2012, 03:09 AM
pranav_s pranav_s is offline
Junior Member
 
Join Date: Jul 2012
Posts: 4
Default P(X) and Error Measure Doubts in Lecture 4

I have a couple of doubts from the 4th Lecture, any clarification would be really appreciated.

1. When talking about P(X), I gather that it was introduced in order to arrive at the Hoeffding's Inequality which is probabilistic in nature. However, even if whe are not making any assumptions about P(X), isn't it true that we are limiting the generalization prospects. As in, if we assume the input set having a particular P(X) we are really regarding the inputs distributed only along those lines. Please clarify if I have got it all wrong!

2.Error measures are supposed to be the average point-wise errors encountered using a hypothesis. How do we really calculate the E_out. considering we do not know the target function, we have taken a random out of sample input. So, e(h(X),f(X)) seems strange as f(X) is really unknown at this Input point.
Reply With Quote
  #2  
Old 07-24-2012, 03:34 AM
yaser's Avatar
yaser yaser is offline
Caltech
 
Join Date: Aug 2009
Location: Pasadena, California, USA
Posts: 1,477
Default Re: P(X) and Error Measure Doubts in Lecture 4

Quote:
Originally Posted by pranav_s View Post
1. When talking about P(X), I gather that it was introduced in order to arrive at the Hoeffding's Inequality which is probabilistic in nature. However, even if whe are not making any assumptions about P(X), isn't it true that we are limiting the generalization prospects. As in, if we assume the input set having a particular P(X) we are really regarding the inputs distributed only along those lines. Please clarify if I have got it all wrong!
Your understanding of the role of P is correct. The problem you foresee if we take a particular P is not really a problem since we do not need to pick a particular P. No points are emphasized or deemphasized by the assumption we made which is the mere existence of such P.

Quote:
2.Error measures are supposed to be the average point-wise errors encountered using a hypothesis. How do we really calculate the E_out. considering we do not know the target function, we have taken a random out of sample input. So, e(h(X),f(X)) seems strange as f(X) is really unknown at this Input point.
The out-of-sample error is inherently unknown. If it were known, we would just minimize it and forget about learning from the data set. However, there are ways to estimate the out-of-sample error through a test or validation set. This will be discussed in detail in a later lecture.
__________________
Where everyone thinks alike, no one thinks very much
Reply With Quote
  #3  
Old 07-24-2012, 10:22 AM
pranav_s pranav_s is offline
Junior Member
 
Join Date: Jul 2012
Posts: 4
Default Re: P(X) and Error Measure Doubts in Lecture 4

Thank you sir, also the course is really interesting.
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 01:59 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.