LFD Book Forum  

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

Reply
 
Thread Tools Display Modes
  #1  
Old 09-11-2013, 02:14 PM
meixingdg meixingdg is offline
Junior Member
 
Join Date: Sep 2013
Posts: 4
Default Chapter 1 - Problem 1.3

I am a bit stuck on part b. I am not sure how to start. Could anyone give a nudge in the right direction?
Reply With Quote
  #2  
Old 09-11-2013, 06:22 PM
magdon's Avatar
magdon magdon is offline
RPI
 
Join Date: Aug 2009
Location: Troy, NY, USA.
Posts: 592
Default Re: Chapter 1 - Problem 1.3

Quote:
Originally Posted by meixingdg View Post
I am a bit stuck on part b. I am not sure how to start. Could anyone give a nudge in the right direction?
The first part is following from the weight update rule for PLA. The second part follows from the first part using a standard induction proof.
__________________
Have faith in probability
Reply With Quote
  #3  
Old 01-14-2015, 12:23 AM
mxcnrawker mxcnrawker is offline
Junior Member
 
Join Date: Jan 2015
Posts: 1
Default Re: Chapter 1 - Problem 1.3

Can you please do the proof for this problem, I can answer the question conceptually but mathematically I'm having a little trouble starting my argument for both part a and part b please
Reply With Quote
  #4  
Old 01-17-2015, 07:20 AM
htlin's Avatar
htlin htlin is offline
NTU
 
Join Date: Aug 2009
Location: Taipei, Taiwan
Posts: 558
Default Re: Chapter 1 - Problem 1.3

Quote:
Originally Posted by mxcnrawker View Post
Can you please do the proof for this problem, I can answer the question conceptually but mathematically I'm having a little trouble starting my argument for both part a and part b please
Part a and the first half of part b can almost be found on p14 here:

http://www.csie.ntu.edu.tw/~htlin/co...02_handout.pdf
__________________
When one teaches, two learn.
Reply With Quote
  #5  
Old 07-20-2015, 02:11 AM
yongxien yongxien is offline
Junior Member
 
Join Date: Jun 2015
Posts: 8
Default Re: Chapter 1 - Problem 1.3

Hi I can solve the problem but I cannot understand how does this show that the perceptron algorithm will converge. Can somone explains to me what does the proof shows? I mean what does each step of the problems mean? Thanks
Reply With Quote
  #6  
Old 07-22-2015, 06:57 AM
htlin's Avatar
htlin htlin is offline
NTU
 
Join Date: Aug 2009
Location: Taipei, Taiwan
Posts: 558
Default Re: Chapter 1 - Problem 1.3

Quote:
Originally Posted by yongxien View Post
Hi I can solve the problem but I cannot understand how does this show that the perceptron algorithm will converge. Can somone explains to me what does the proof shows? I mean what does each step of the problems mean? Thanks
The proof essentially shows that the (normalized) inner product between \mathbf{w}_t and the separating weights will be larger and larger in each iteration. But the normalized inner product is upper bounded by 1 and cannot be arbitrarily large. Hence PLA will converge.
__________________
When one teaches, two learn.
Reply With Quote
  #7  
Old 08-18-2015, 03:07 AM
elyakim elyakim is offline
Junior Member
 
Join Date: Aug 2015
Posts: 2
Default Re: Chapter 1 - Problem 1.3

Despite the slides I still have difficulty reading the equations.

In my PLA program weights are updated by "the difference between the 'target function line' and x2" for a misclassified example from a 2-dimensional space.

Example target function line: 2 + 3x. If x1 = 3 en x2 = 9, y = 9- (2+3*3) = -2
If misclassified the weights would be updated like: wt+1 = wt + x1 * -2
The method above maybe omits advantages of vector computation(?) as seen in the slides, but I was happy the simulation worked at all

The theoretic approach of this course seems more useful in the long term than 'simply learning to type methods', but for me is new and challenging.

So my questions are:
- is p a random symbol? I can't find it in the overview.
- does min1 < n < N stand for the sum of function (x) in range N?
- is yn the positive or negative difference between the target line and coordinate x2 (staying with the 2-dimensional graphical model)?
- I understand a little simple linear algebra for linear regression. Are vector computations making the understanding of this PLA equation easier?

Thanks in advance!
Reply With Quote
  #8  
Old 03-23-2016, 01:21 AM
ntvy95 ntvy95 is offline
Member
 
Join Date: Jan 2016
Posts: 37
Default Re: Chapter 1 - Problem 1.3

Hi, I am stuck at the part (e). I have two questions:

1 - Is R' a typo? If R' is R then:

2 - Refer to (b), I observe that:



Refer to (c), I observe that:



But I think that happens only when t <= 1? Am I mistaken somewhere?
Attached Thumbnails
gif (2).gif   gif (3).gif   gif (4).gif  
Reply With Quote
  #9  
Old 03-23-2016, 04:17 AM
MaciekLeks MaciekLeks is offline
Member
 
Join Date: Jan 2016
Location: Katowice, Upper Silesia, Poland
Posts: 17
Default Re: Chapter 1 - Problem 1.3

Quote:
Originally Posted by ntvy95 View Post
Hi, I am stuck at the part (e). I have two questions:

1 - Is R' a typo? If R' is R then:

2 - Refer to (b), I observe that:



Refer to (c), I observe that:



But I think that happens only when t <= 1? Am I mistaken somewhere?
1. I assumed while performing a proof that ',' is just a comma char, not a typo
2. (c) works well for t>=0. Do not refer from (b) to (c). Try to refer to the previously proven inequality (so, from (c) to (b)).
Reply With Quote
  #10  
Old 03-23-2016, 05:04 AM
ntvy95 ntvy95 is offline
Member
 
Join Date: Jan 2016
Posts: 37
Default Re: Chapter 1 - Problem 1.3

Quote:
Originally Posted by MaciekLeks View Post
1. I assumed while performing a proof that ',' is just a comma char, not a typo
2. (c) works well for t>=0. Do not refer from (b) to (c). Try to refer to the previously proven inequality (so, from (c) to (b)).
Aha! I see the point now! Thank you very much!!!
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 02:08 AM.


Powered by vBulletin® Version 3.8.3
Copyright ©2000 - 2017, 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.