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-   Chapter 1 - The Learning Problem (http://book.caltech.edu/bookforum/forumdisplay.php?f=108)
-   -   Chapter 1 - Problem 1.3 (http://book.caltech.edu/bookforum/showthread.php?t=4413)

 meixingdg 09-11-2013 02:14 PM

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?

 magdon 09-11-2013 06:22 PM

Re: Chapter 1 - Problem 1.3

Quote:
 Originally Posted by meixingdg (Post 11481) 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.

 mxcnrawker 01-14-2015 12:23 AM

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 :bow:

 htlin 01-17-2015 07:20 AM

Re: Chapter 1 - Problem 1.3

Quote:
 Originally Posted by mxcnrawker (Post 11902) 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 :bow:
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

 yongxien 07-20-2015 02:11 AM

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

 htlin 07-22-2015 06:57 AM

Re: Chapter 1 - Problem 1.3

Quote:
 Originally Posted by yongxien (Post 11983) 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.

 elyakim 08-18-2015 03:07 AM

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?

 ntvy95 03-23-2016 01:21 AM

Re: Chapter 1 - Problem 1.3

3 Attachment(s)
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:

http://book.caltech.edu/bookforum/at...1&d=1458721054

Refer to (c), I observe that:

http://book.caltech.edu/bookforum/at...1&d=1458720991

But I think that http://book.caltech.edu/bookforum/at...1&d=1458721179 happens only when t <= 1? Am I mistaken somewhere?

 MaciekLeks 03-23-2016 04:17 AM

Re: Chapter 1 - Problem 1.3

Quote:
 Originally Posted by ntvy95 (Post 12300) 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: http://book.caltech.edu/bookforum/at...1&d=1458721054 Refer to (c), I observe that: http://book.caltech.edu/bookforum/at...1&d=1458720991 But I think that http://book.caltech.edu/bookforum/at...1&d=1458721179 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)).

 ntvy95 03-23-2016 05:04 AM

Re: Chapter 1 - Problem 1.3

Quote:
 Originally Posted by MaciekLeks (Post 12303) 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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