LFD Book Forum  

Go Back   LFD Book Forum > Course Discussions > Online LFD course > Homework 4

Reply
 
Thread Tools Display Modes
  #1  
Old 05-01-2012, 06:03 PM
markweitzman markweitzman is offline
Invited Guest
 
Join Date: Apr 2012
Location: Las Vegas
Posts: 69
Default HW 4 question3

I am confused about question3 - are they not all above 1 and therefore essentially equivalent in the range 2-8. Or did I do the calculation incorrectly?

Mark Weitzman
Reply With Quote
  #2  
Old 05-01-2012, 06:18 PM
Hillbilly Hillbilly is offline
Invited Guest
 
Join Date: Mar 2012
Location: West Virginia
Posts: 45
Default Re: HW 4 question3

I agree with the implication of your question -- isn't an epsilon greater than 1 essentially meaningless, making them all equivalent in that sense? Nevertheless, I got distinctly different curves for the four choices, strictly ordered, so I answered on that basis, and apparently that was the right perspective. Devroye gave me weird results on both extremes of N; N=2 particularly bizarre, but I may have a bug in it I haven't found yet.
Reply With Quote
  #3  
Old 05-01-2012, 06:32 PM
markweitzman markweitzman is offline
Invited Guest
 
Join Date: Apr 2012
Location: Las Vegas
Posts: 69
Default Re: HW 4 question3

Well I thought like you did and calculated similar results, when I realized that all equivalent if all greater than 1 seems like the best result.

Mark Weitzman
Reply With Quote
  #4  
Old 05-01-2012, 08:45 PM
silvrous silvrous is offline
Member
 
Join Date: Apr 2012
Posts: 24
Default Re: HW 4 question3

I also got values larger than 1 for all of them, and therefore considered them to be equally meaningless for small N...
Reply With Quote
  #5  
Old 05-01-2012, 11:52 PM
rohanag rohanag is offline
Invited Guest
 
Join Date: Apr 2012
Posts: 94
Default Re: HW 4 question3

how are the recursive questions (part c and d) to be plotted?

Last edited by rohanag; 05-01-2012 at 11:52 PM. Reason: clarity
Reply With Quote
  #6  
Old 05-02-2012, 01:07 AM
IamMrBB IamMrBB is offline
Invited Guest
 
Join Date: Apr 2012
Posts: 107
Default Re: HW 4 question3

I have the same question/remark as silvrous and markweitzman. Since epsilon bounds the absolute difference of two probabilities/probability measures/frequencies (at least that is what I understood from the class and a quick google lookup) a statement of epsilon < 3 (for example) is equivalent to the stamement epsilon <= 1. Since all bounds gave numbers in the ball park 3, I reasoned they are all equivalent to bounds epsilon <= 1, i.e. with this small number of examples we cannot say anything about Eout, at least not with a delta of 0.05 per the question.

I have to admit that I thougth long and hard about the what was the intention of the question: just to test if we can calculate these scary looking formulas, or to test our understanding of learning (in particular understanding that you need a minimum amount of data before you can make strong (delta = 5%) statements about the out of sample). Since the calculation aspect was already tested in q2, I hoped and guessed that q3 was aiming at the other aspect.

In the end I therefore went for answer e ("they are all equivalent"), which I thought was the most correct, although there was indeed a chance the question was intended differently.

Professor, or any other expert on the subject, am I correct in my assumption about that epsilon < 3 is equivalent to epsilon <= 1?
Reply With Quote
  #7  
Old 05-02-2012, 01:36 AM
lucifirm lucifirm is offline
Member
 
Join Date: Apr 2012
Posts: 20
Unhappy Re: HW 4 question3

What I did was to create a vector \epsilon of the same size of N, but varying from 0 to 1. I don't know if this is the best approach, but it helped me to plot the curves. The problem is I thought I had to chose only one correct answer, so I could not choose c or d, because for me they were both correct for large N.


I don't know if this will work, but here's a link to the figure.

https://docs.google.com/open?id=0By0...FRkclhvRnZMd2s
Reply With Quote
  #8  
Old 05-02-2012, 04:23 AM
rohanag rohanag is offline
Invited Guest
 
Join Date: Apr 2012
Posts: 94
Default Re: HW 4 question3

thanks lucifirm, do you mean, you tried different values of \epsilon and then compared the left hand side and right hand side of the equations?
you'r right both c and d are the answers for large value of N. But for small values of N, c is the correct answer according to he key.
Reply With Quote
  #9  
Old 05-02-2012, 04:34 AM
elkka elkka is offline
Invited Guest
 
Join Date: Apr 2012
Posts: 57
Default Re: HW 4 question3

I first thought the same thing about 1. But then, where do we see \varepsilon? It is the measure of difference between E_in and E_out, which can be small, and can be big depending on the experiment. Suppose you are talking about an experiment with very large numbers, like the number of minutes people use in a month on a cell phone (which, say, average 200). Than it is totally meaningful to consider a prediction that assures you that |E_{in} -E_{out}|<2 (or 5, or 10) with probability 0.95. So, it totally makes sense to rate the bounds even if they all are >1
Reply With Quote
  #10  
Old 05-02-2012, 04:38 AM
elkka elkka is offline
Invited Guest
 
Join Date: Apr 2012
Posts: 57
Default Re: HW 4 question3

rohanag, the recursive bounds can easily be solved for \varepsilon, as 1. they are, essentially, quadratic equations, and 2. only one root is of interest, as \varepsilon>0. By solving the equations you get

(c) \varepsilon = \frac{1}{N}+\sqrt{\frac{1}{N^2}+\frac{1}{N}\ln{\frac{6m_\mathcal{H}(2N)}{\delta}}};

(d) \varepsilon = \frac{1}{N-2}+\sqrt{\frac{1}{(N-2)^2}+\frac{1}{2(N-2)}\ln{\frac{4m_\mathcal{H}(N^2)}{\delta}}}.
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 07:47 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.