LFD Book Forum  

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

Reply
 
Thread Tools Display Modes
  #1  
Old 04-20-2013, 11:47 PM
arcticblue arcticblue is offline
Member
 
Join Date: Apr 2013
Posts: 17
Default Q6

I am unsure what is meant by 2 intervals. Is this a valid layout for 2 intervals?
x|o|x|o|x
Or does it mean?
x|o|x

And to find the breakpoint I presume all I need to do is find a layout where the N points can't be successfully put into the M intervals.
eg
N=4 (xoxo) would be a breakpoint for the second option above if my understanding is correct.

Since there aren't any questions about Q6/Q8 I'm guessing I've just misunderstood the problem or haven't understood part of the lecture. Any advice would be appreciated.
Reply With Quote
  #2  
Old 04-20-2013, 11:56 PM
marek marek is offline
Member
 
Join Date: Apr 2013
Posts: 31
Default Re: Q6

There are a few other threads about the multiple interval questions, so you're not alone. In summary, both of your scenarios are valid, depending on the context. But rather than repeat what is in those threads, it's perhaps best that you check them out directly.
Reply With Quote
  #3  
Old 04-21-2013, 12:06 AM
marek marek is offline
Member
 
Join Date: Apr 2013
Posts: 31
Default Re: Q6

I'll give one concrete numerical example to hopefully set you on the right path.

Lets say I am considering N = 3 and pick points {1, 7, 11}. Can I find a way to set up two intervals to get all possible 2^3 = 8 possible dichotomies? By your short hand I'm assuming o represents +1 and x represents -1.

If I want the arrangment xox, that means 1 and 11 have to be outside my choices for intervals and 7 has to be inside. So one particular choice of intervals would be [5,9] and [99,100]. Another would be [5,8] and [6,10]. You can go easily verify that all possible 2^3 arrangements are possible. The only trick here is that you're restricted by the geometry of an interval, meaning it starts at one particular value, ends at another, and contains every point in between.
Reply With Quote
  #4  
Old 04-21-2013, 01:58 AM
arcticblue arcticblue is offline
Member
 
Join Date: Apr 2013
Posts: 17
Default Re: Q6

Okay so it seems like my understanding is correct. And if we take the case of M=1 which should match up with the example given in lecture 5. Here it's possible to find a setup which splits N=3 correctly for all 8 combinations. So then for M=1 the breakpoint must be at least 4 since 3 points can be satisfied. But then in Q8 the general case M=1 must be 4 or greater since the breakpoint is 4 or more, however for M=1 the largest option is a breakpoint of 3.

So I guess Q8 is confusing me for Q6. I must be misunderstanding something except I think I understand how the breakpoint number works and I think my understanding of the example in the lecture is correct. Any ideas on what I've missed?
Reply With Quote
  #5  
Old 04-21-2013, 09:50 AM
marek marek is offline
Member
 
Join Date: Apr 2013
Posts: 31
Default Re: Q6

Quote:
Originally Posted by arcticblue View Post
Okay so it seems like my understanding is correct. And if we take the case of M=1 which should match up with the example given in lecture 5. Here it's possible to find a setup which splits N=3 correctly for all 8 combinations. So then for M=1 the breakpoint must be at least 4 since 3 points can be satisfied. But then in Q8 the general case M=1 must be 4 or greater since the breakpoint is 4 or more, however for M=1 the largest option is a breakpoint of 3.

So I guess Q8 is confusing me for Q6. I must be misunderstanding something except I think I understand how the breakpoint number works and I think my understanding of the example in the lecture is correct. Any ideas on what I've missed?
For M=1, N = 3, the breakpoint is not 4. It is 3. Double check all 8 configurations. You should find one that you cannot obtain with just 1 interval.
Reply With Quote
  #6  
Old 04-21-2013, 03:42 PM
arcticblue arcticblue is offline
Member
 
Join Date: Apr 2013
Posts: 17
Default Re: Q6

Thanks Marek I now see what I was doing wrong. Everything makes sense now.
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 09:30 AM.


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.