Chapter 1 - Problem 1.3

[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?

[magdon]

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.

[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

[htlin]

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

[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

[htlin]

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.