#1




PLA  Need Guidance
Greetings!
I am working on the Perceptron part of the homework, and having spent several hours on it, I'd like to know if I am proceeding in the right direction: 1) My implementation converges in 'N' iterations. This looks rather fishy. Any comments would be appreciated. (Otherwise I may have to start over :( maybe in a different programming language) 2) I don't understand the Pr( f(x) != g(x) ) expression  what exactly does this mean? Once the algorithm has converged, presumable f(x) matches g(x) on all data, so the difference is zero. Thanks. Samir 
#2




Re: PLA  Need Guidance
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#3




Re: PLA  Need Guidance
If we try to evaluate Pr(f(x)!=g(x)) experimentaly how many random verification points should we use to get a significant answear?
I am tempted to believe that Hoeffding's inequality is applicable in this case to a single experiment but since we are averaging out over very many experiments I'm not sure on how to choose the amount of those verification data points (I ultimately worked with 10000 per experiment just to be sure). 
#4




Re: PLA  Need Guidance
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#5




Re: PLA  Need Guidance
How would you determine f(x) == g(x) exactly  since the set of possible hypotheses is infinite (3 reals), wouldn't Pr(f(x) != g(x)) == 1? Obviously you could choose some arbitrary epsilon but then that wouldn't be "exactly."

#6




Re: PLA  Need Guidance
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#7




Re: PLA  Need Guidance
Hoeffding inequality given in same lesson can help to choose number of points. g(x)!=f(x) can be thinked as red marble

#8




Re: PLA  Need Guidance
I still don't understand this Pr() function. Given two (linear) functions f and g, what is the Pr() of f and g?
Thanks...Neil 
#9




Re: PLA  Need Guidance
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BTW, anyone who wants to refresh some of the prerequisite material for the course, here are some recommendations: http://book.caltech.edu/bookforum/showthread.php?t=3720
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#10




Re: PLA  Need Guidance
Sir
If I understand correctly, we are using N = 10 training points out of a randomly generated x points according to the target function f for perceptron learning and Pr(f(x) != g(x)) should be calculated considering all x points and not just the training data. Am I right ? 
Tags 
convergence, iterations, perceptron, pla 
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