#1




Confused on question 6.
Edit: Solved it, the story below is no longer relevant.
I'm confused about how one is supposed to calculate the score exactly. My biggest confusion seems to stem from the misunderstanding of what a 'point' is. Is a point one of the input vectors? so 101, 110 and 111 are 3 points? So then g[a], returns 1 for all three points would mean that: Code:
101  1 110  1 111  1 Code:
101  0 110  0 111  0 Code:
101  0 110  0 111  1 Code:
101  1 110  1 111  0 Code:
101  0 110  0 111  1 I'm utterly confused by the question. :/ 
#2




Re: Confused on question 6.
A point is a data point, so these are 3 points. For each possible target function, there is a number of agreements (0,1,2 or3) with your hypothesis on these 3 points. We are keeping a tally of the number of agreements as we go through all possible target functions.
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#3




Re: Confused on question 6.
Quote:
Thank you for the response, I was approaching the question completely wrong but solved it in the meantime. 
#4




Re: Confused on question 6.
You are welcome. Everyone is encouraged to ask questions, big or small.
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#5




Re: Confused on question 6.
Sorry I'm struggling a bit understanding the framework here. Maybe it's just terminology. What is the difference between a "possible target function" and a "hypothesis" ? I thought that they were equivalent, but it does not seem to be the case  a hypothesis must agree with a target function.

#6




Re: Confused on question 6.
Quote:
Hypotheses are the products of learning that try to approximate the target function. In this problem, we prescribe different learning scenarios that result in different hypotheses, then attempt to grade these hypotheses. We grade them according to how well each of them approximates the target function. The twist is that we consider all possible target functions and grade the hypothesis according to how well it approximates each of these possible targets.
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#7




Re: Confused on question 6.
Thank you  I understand now. For some reason it took me a leap to figure out how to build the "target function" such that it could be measured as stated in the problem. Originally, I had a list of 8 "functions"  but each function was just simply one of the 8 permutations where a permutation was an input point and a possible output.

#8




Re: Confused on question 6.
Hi,
What's a possible target function? Is that a combination of boolean operators? How do you come up with the formula 2^2^3 for total number of possibl target functions for 3 boollean inputs? Thank you. 
#9




Re: Confused on question 6.
Quote:
There are points in the input space here, which are all binary combinations of the 3 input variables from to . For each of these points, a Boolean function may return 0 or 1; hence two possibilities. Therefore, for all 8 points, a Boolean function may return (8 times) possibilities, which gives us the number of different Boolean functions .
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#10




Re: Confused on question 6.
Quote:
So, yvalues on points in D are not used in the answer? Seems, number of matches do not affected which hypothesis I choose  any hypothesis produce same number of matches Binomial(3, #matches) on these 3 points. Seems too easy, like dangerous trap or puzzle with catchy answer  if number of matches is always the same, why to define some complicated functions of matches and give Yvalues on other five points. Or I got something wrong : May be matches outside these 3 points (matches inside D) should be counted too? 
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