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Old 09-11-2013, 03:14 PM
meixingdg meixingdg is offline
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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?
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  #2  
Old 09-11-2013, 07:22 PM
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magdon magdon is offline
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Default Re: Chapter 1 - Problem 1.3

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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.
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Old 01-14-2015, 01:23 AM
mxcnrawker mxcnrawker is offline
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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
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Old 01-17-2015, 08:20 AM
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htlin htlin is offline
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Default Re: Chapter 1 - Problem 1.3

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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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Old 07-20-2015, 03:11 AM
yongxien yongxien is offline
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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
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Old 07-22-2015, 07:57 AM
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htlin htlin is offline
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Default Re: Chapter 1 - Problem 1.3

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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.
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