LFD Book Forum Hoeffding inequality for multiple classifiers
 User Name Remember Me? Password
 Register FAQ Calendar Mark Forums Read

 Thread Tools Display Modes
#1
02-22-2013, 01:51 PM
 cls2k Junior Member Join Date: May 2012 Posts: 5
Hoeffding inequality for multiple classifiers

I'm having some trouble understanding the case of applying Hoeffding to the case of multiple classifier (Bins). Shouldn't the final picked hypothesis g* still be bound by Hoeffding's inequality since its just like any other hypothesis in the set? How does the process of picking the hypothesis based on the data affect the Hoeffding's bound? What if I pick the worst hypothesis instead of the best one? shouldn't hoeffding's bound apply to that too?

While I understand the mathematics behind the union bound, it seems unintuitive that the bond on g* should be a union of all the bonds of h() in the set since the final g* does not have anything to do with the other unpicked hypothesis.

I do understand the coin example. since the chance of getting 10 heads in a row for one coin is very low but its actually high if you repeat the experiment 1000 times. However I'm unsure as to how this relates to the learning scenario. Getting 10 heads on a sample would be equivelant to getting an Ein of 0. But its mentioned again and again that this is a "bad" event. How does this have anything to do with the Hoeffding bound?

Any insight into this will be greatly appreciated.
#2
02-22-2013, 04:36 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,478
Re: Hoeffding inequality for multiple classifiers

Quote:
 Originally Posted by cls2k I'm having some trouble understanding the case of applying Hoeffding to the case of multiple classifier (Bins). Shouldn't the final picked hypothesis g* still be bound by Hoeffding's inequality since its just like any other hypothesis in the set? How does the process of picking the hypothesis based on the data affect the Hoeffding's bound? What if I pick the worst hypothesis instead of the best one? shouldn't hoeffding's bound apply to that too?
The assumptions used to prove Hoeffding necessitate that not depend on the sample, which is violated when is the hypothesis since it was chosen according to the sample. Without this assumption, the proof doesn't go through.

Quote:
 While I understand the mathematics behind the union bound, it seems unintuitive that the bond on g* should be a union of all the bonds of h() in the set since the final g* does not have anything to do with the other unpicked hypothesis.
It is just a bound that can be asserted without making assumptions about what depends on what, so it is valid even if more careful analysis in a particular case yields a tighter bound.

Quote:
 I do understand the coin example. since the chance of getting 10 heads in a row for one coin is very low but its actually high if you repeat the experiment 1000 times. However I'm unsure as to how this relates to the learning scenario. Getting 10 heads on a sample would be equivelant to getting an Ein of 0. But its mentioned again and again that this is a "bad" event. How does this have anything to do with the Hoeffding bound?
Equate getting a head with making an error, and that explains the 'bad event' part. The relation to learning is that the sample suggests the coin is not fair when in fact it is, which means generalization is poor.
__________________
Where everyone thinks alike, no one thinks very much

 Tags hoeffding's inequality

 Thread Tools Display Modes Linear Mode

 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 Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home General     General Discussion of Machine Learning     Free Additional Material         Dynamic e-Chapters         Dynamic e-Appendices Course Discussions     Online LFD course         General comments on the course         Homework 1         Homework 2         Homework 3         Homework 4         Homework 5         Homework 6         Homework 7         Homework 8         The Final         Create New Homework Problems Book Feedback - Learning From Data     General comments on the book     Chapter 1 - The Learning Problem     Chapter 2 - Training versus Testing     Chapter 3 - The Linear Model     Chapter 4 - Overfitting     Chapter 5 - Three Learning Principles     e-Chapter 6 - Similarity Based Methods     e-Chapter 7 - Neural Networks     e-Chapter 8 - Support Vector Machines     e-Chapter 9 - Learning Aides     Appendix and Notation     e-Appendices

All times are GMT -7. The time now is 11:59 AM.

 Contact Us - LFD Book - Top

Powered by vBulletin® Version 3.8.3
Copyright ©2000 - 2020, 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.