LFD Book Forum  

Go Back   LFD Book Forum > Course Discussions > Online LFD course > Homework 3

Reply
 
Thread Tools Display Modes
  #1  
Old 04-21-2013, 07:56 AM
nkatz nkatz is offline
Junior Member
 
Join Date: Apr 2013
Posts: 4
Default Why 2^N Makes Learning Unfeasible

I was going to ask what was wrong with 2^N growth function since 2^Ne^{-N}\rightarrow 0 but I think I figured it out:
The right hand side of the modified Hoeffding is really 2^{2N}/e^{\epsilon^2N/8} which goes to 0 only if 2^2/e^{\epsilon^2/8}<1, which would require \epsilon>3.3 which is meaningless since Ein and Eout are between 0 and 1.
Is this argument correct?
Reply With Quote
  #2  
Old 04-21-2013, 08:02 AM
Michael Reach Michael Reach is offline
Senior Member
 
Join Date: Apr 2013
Location: Baltimore, Maryland, USA
Posts: 71
Default Re: Why 2^N Makes Learning Unfeasible

I think that's right. You want to be able to make \epsilon small.

Note that this doesn't mean that learning is not feasible, only that this inequality won't help you prove that it is. There might be some other way to bound growth. The professor already hinted that there are sometimes more ways, based on an "average" growth function that works for "most" cases.
Reply With Quote
  #3  
Old 04-21-2013, 08:51 PM
jlaurentum jlaurentum is offline
Member
 
Join Date: Apr 2013
Location: Venezuela
Posts: 41
Default Re: Why 2^N Makes Learning Unfeasible

If M=2^N, then you'd have 2\left(\frac{2}{e^{\varepsilon^2}}\right)^N on the right hand side. Any value of \varepsilon that makes the exponential denominator smaller than the numerator of 2 would make the whole expression bigger than 2, which is meaningless for a probabilistic bound. The case in point, any epsilon smaller than 0.83 makes this upper hoeffding bound useless. Of course, 0.83 is an useless value for epsilon because you want to be able to make epsilon as close to 0 as you want.
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 08:06 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.