
#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
Quote:
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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
Quote:
__________________
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#7




Re: PLA  Need Guidance
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Each line can crosses two of the sides of the square. (I suppose it could also go right through a corner, but not likely). Handling all the possible combinations of the two lines is a lot of work. In another thread I discussed how I did it, only counting, and computing the area of, cases where both lines go through the top and bottom. That is about 30% in my tests. By symmetry, there should also be 30% where both go through the left and right sides of the square The remaining cases might have a little less area, but I based my answer on just the lines going through the top and bottom of the square. Seemed more interesting than the choose random point method. 
#8




Re: PLA  Need Guidance
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Can you kindly explain how we can calculate this number. How can we ensure that the number is "sufficiently large" Thanks, Bipin 
#9




Re: PLA  Need Guidance
Quote:
__________________
Where everyone thinks alike, no one thinks very much 
#10




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

Tags 
convergence, iterations, perceptron, pla 
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