LFD Book Forum Chapter 1 - Problem 1.3
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#1
09-11-2013, 03:14 PM
 meixingdg Junior Member Join Date: Sep 2013 Posts: 4
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?
#2
09-11-2013, 07:22 PM
 magdon RPI Join Date: Aug 2009 Location: Troy, NY, USA. Posts: 595
Re: Chapter 1 - Problem 1.3

Quote:
 Originally Posted by meixingdg 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.
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#3
01-14-2015, 01:23 AM
 mxcnrawker Junior Member Join Date: Jan 2015 Posts: 1
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
#4
01-17-2015, 08:20 AM
 htlin NTU Join Date: Aug 2009 Location: Taipei, Taiwan Posts: 601
Re: Chapter 1 - Problem 1.3

Quote:
 Originally Posted by mxcnrawker 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
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#5
07-20-2015, 03:11 AM
 yongxien Junior Member Join Date: Jun 2015 Posts: 8
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
#6
07-22-2015, 07:57 AM
 htlin NTU Join Date: Aug 2009 Location: Taipei, Taiwan Posts: 601
Re: Chapter 1 - Problem 1.3

Quote:
 Originally Posted by yongxien 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 and the separating weights will be larger and larger in each iteration. But the normalized inner product is upper bounded by and cannot be arbitrarily large. Hence PLA will converge.
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#7
08-18-2015, 04:07 AM
 elyakim Junior Member Join Date: Aug 2015 Posts: 2
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!
#8
03-23-2016, 02:21 AM
 ntvy95 Member Join Date: Jan 2016 Posts: 37
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?
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#9
03-23-2016, 05:17 AM
 MaciekLeks Member Join Date: Jan 2016 Location: Katowice, Upper Silesia, Poland Posts: 17
Re: Chapter 1 - Problem 1.3

Quote:
 Originally Posted by ntvy95 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)).
#10
03-23-2016, 06:04 AM
 ntvy95 Member Join Date: Jan 2016 Posts: 37
Re: Chapter 1 - Problem 1.3

Quote:
 Originally Posted by MaciekLeks 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!!!

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