HW 4 question3
I am confused about question3  are they not all above 1 and therefore essentially equivalent in the range 28. Or did I do the calculation incorrectly?
Mark Weitzman 
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I agree with the implication of your question  isn't an epsilon greater than 1 essentially meaningless, making them all equivalent in that sense? Nevertheless, I got distinctly different curves for the four choices, strictly ordered, so I answered on that basis, and apparently that was the right perspective. Devroye gave me weird results on both extremes of N; N=2 particularly bizarre, but I may have a bug in it I haven't found yet.

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Well I thought like you did and calculated similar results, when I realized that all equivalent if all greater than 1 seems like the best result.
Mark Weitzman 
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I also got values larger than 1 for all of them, and therefore considered them to be equally meaningless for small N...

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how are the recursive questions (part c and d) to be plotted?

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I have the same question/remark as silvrous and markweitzman. Since epsilon bounds the absolute difference of two probabilities/probability measures/frequencies (at least that is what I understood from the class and a quick google lookup) a statement of epsilon < 3 (for example) is equivalent to the stamement epsilon <= 1. Since all bounds gave numbers in the ball park 3, I reasoned they are all equivalent to bounds epsilon <= 1, i.e. with this small number of examples we cannot say anything about Eout, at least not with a delta of 0.05 per the question.
I have to admit that I thougth long and hard about the what was the intention of the question: just to test if we can calculate these scary looking formulas, or to test our understanding of learning (in particular understanding that you need a minimum amount of data before you can make strong (delta = 5%) statements about the out of sample). Since the calculation aspect was already tested in q2, I hoped and guessed that q3 was aiming at the other aspect. In the end I therefore went for answer e ("they are all equivalent"), which I thought was the most correct, although there was indeed a chance the question was intended differently. Professor, or any other expert on the subject, am I correct in my assumption about that epsilon < 3 is equivalent to epsilon <= 1? 
Re: HW 4 question3
What I did was to create a vector of the same size of N, but varying from 0 to 1. I don't know if this is the best approach, but it helped me to plot the curves. The problem is I thought I had to chose only one correct answer, so I could not choose c or d, because for me they were both correct for large N.
I don't know if this will work, but here's a link to the figure. https://docs.google.com/open?id=0By0...FRkclhvRnZMd2s 
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thanks lucifirm, do you mean, you tried different values of \epsilon and then compared the left hand side and right hand side of the equations?
you'r right both c and d are the answers for large value of N. But for small values of N, c is the correct answer according to he key. 
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thanks elkka , i don't know that I was thinking :(

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Therefore, it is quite impossible for epsilon to ever exceed 1. 
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To see that your example probably doesn't make sense (IMHO): replace the minutes in your example with either nanoseconds or, on the other hand, ages, and you would get very different numbers on the left side of the equation (i.e. epsilon) while it wouldn't make a difference for the right side of the equation. This can't be right (it would e.g. be unlikely that E_in and E_out are 60 seconds apart but likely that they are a minute apart?!): it would make the inequalities meaningless. Also on the slides of lecture 6, it is fractions (in)correctly classified that are used for the VapnikChervonenkis Inequality. Dislaimer: I'm not an expert on the matter, and perhaps I miss a/the point somewhere, so hope we'll get a verdict by the course staff. 
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You know, I think you are right. We are indeed only talking about classification problem, so E_in and E_out must be <= 1.

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Here is my view which can be wrong. Refer to lecture 4, slides 7 onwards.
Ein and Eout are the average of the error measure per point. And it is up to the user to choose the error measure. So Ein and Eout are just numbers and not probabilities. And so epsilon which is the difference between the two, is also a number. Also see lecture 8, slides 15 and 20: Eout = bias + variance = 0.21 + 1.69 > 1 
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Could someone from the course staff perhaps weigh in on this? There seem to be two equally valid theories....

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It suggested to use the simple approximate bound N^d_vc for the growth function, if N > d_vc. In Problem 3, N=5<d_vc=50. Should we still use N^d_vc as an approximation for the growth function? Or, maybe it is more reasonable to use 2^N, assuming that H is complex enough?

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