LFD Book Forum  

Go Back   LFD Book Forum > Book Feedback - Learning From Data > Chapter 1 - The Learning Problem

 
 
Thread Tools Display Modes
Prev Previous Post   Next Post Next
  #1  
Old 01-31-2013, 12:57 AM
scottedwards2000 scottedwards2000 is offline
Junior Member
 
Join Date: Jan 2013
Posts: 9
Default Is the Hoeffding Inequality really valid for each bin despite non-random sampling?

The multiple bin analogy of picking the best h is a very helpful way of visualizing the situation, and I totally get how the union bound sets an upper limit on the probability of exceeding the error threshold. What I am actually questioning is whether those individual probabilities that compose the union bound are correct. I can see that they are just the individual Hoeffding Inequalities for each h, but is the Hoeffding Inequality really valid for all those h's in spite of the fact that we are NOT taking random samples from each "bin"? We are only picking our marbles (x's) ONCE, and then re-picking the same marbles from each bin (yes, the red-green colors of those marbles can change, based on the specific h, but aren't they the same marbles (x's)?).

Thanks for your help!
Reply With Quote
 

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 06:39 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.