LFD Book Forum Chapter 1 - Exercise 1.9

#1
09-11-2013, 10:31 AM
 goldsj3 Junior Member Join Date: Sep 2013 Posts: 1
Chapter 1 - Exercise 1.9

Based on the marbles example, I understand that u is the probability of choosing a red marble from the bin of marbles and v is the fraction of red marbles in the sample of chosen marbles. And I think that the LHS of the Hoeffding Inequality represents the probability of v deviating from u being greater than the error bar epsilon. Now, I am not sure how I should choose an epsilon to evaluate this probability and where I should begin. Can someone point me in the right direction?
#2
09-11-2013, 12:31 PM
 magdon RPI Join Date: Aug 2009 Location: Troy, NY, USA. Posts: 595
Re: Chapter 1 - Exercise 1.9

If and , it implies that (any number slightly less than 0.8). By the implication bound,

By looking at the RHS, one can identify for applying the Hoeffding bound.
__________________
Have faith in probability
#3
09-15-2015, 02:51 PM
 eshmrt Junior Member Join Date: Sep 2015 Posts: 2
Re: Chapter 1 - Exercise 1.9

Since we're only looking at epsilon applied in one direction, meaning that we're only interested in nu being mu - 0.8 and not mu + 0.8, should we drop the leading 2 from the bound calculation? I'm not sure if I'm interpreting this bound correctly or simply overthinking things.
#4
09-21-2015, 04:27 PM
 magdon RPI Join Date: Aug 2009 Location: Troy, NY, USA. Posts: 595
Re: Chapter 1 - Exercise 1.9

You are right. If al you want is the "one sided deviation", you could drop the factor of 2. However keeping the factor of 2 is a worse but still valid bound.

Quote:
 Originally Posted by eshmrt Since we're only looking at epsilon applied in one direction, meaning that we're only interested in nu being mu - 0.8 and not mu + 0.8, should we drop the leading 2 from the bound calculation? I'm not sure if I'm interpreting this bound correctly or simply overthinking things.
__________________
Have faith in probability
#5
11-05-2017, 07:17 AM
 henry2015 Member Join Date: Aug 2015 Posts: 31
Re: Chapter 1 - Exercise 1.9

Quote:
 Originally Posted by magdon If and , it implies that (any number slightly less than 0.8). By the implication bound, By looking at the RHS, one can identify for applying the Hoeffding bound.
Hi, I am a bit confused.

I thought when it says , it means because smallest probably is 0; hence, ....I am sure I miss something.

Any pointer?

Thanks!
#6
09-11-2018, 03:03 PM
 mike7 Junior Member Join Date: Sep 2018 Posts: 1
Re: Chapter 1 - Exercise 1.9

Quote:
 Originally Posted by magdon If and , it implies that (any number slightly less than 0.8). By the implication bound, By looking at the RHS, one can identify for applying the Hoeffding bound.
If I am understanding the implications of this correctly, is too large within the Hoeffding bound, correct? One would need to select some , perhaps arbitrarily?

 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 09:01 AM.