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 Code:
101  0 Code:
101  0 Code:
101  1 Code:
101  0 I'm utterly confused by the question. :/ 
Re: Confused on question 6.
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Thank you for the response, I was approaching the question completely wrong but solved it in the meantime. :) 
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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. 
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.

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. 
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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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Re: Confused on question 6.
no worries! :)
x_n is a vector of 3 values. x_n = [x_n1, x_n2, x_n3]. Each value can be 0 or 1. So there could 8 (2 * 2 * 2) distinct set of x_n vector values. In digital logic, the boolean values true/false are represented as 1 and 0. 1 is true and 0 is false. in 6c) The problem defines g as XOR: "if the number of 1's in x is odd, g returns 1; if it is even g returns 0". Consider x_n = [1,0,0] then, the number of 1 in this example is 1, which is odd, so g returns 1. so g(x_n) = 1. 
Re: Confused on question 6.
Sorry, I am also a bit confused on question #6.
Specifically, I want to understand 6(d). It says g returns the opposite of the XOR function: if the number of 1s is odd, it returns 0, otherwise it returns 1. Here is what I am unclear on. Is the meaning of 6(d) that the hypothesis on set D is simply D, and then outside of D it is this opposite of XOR function? Or is 6(d) trying to define a hypothesis for the entire dataset? Clearly, 6(d) does the exact wrong thing on D, so by definition there are no target functions that satisfy 6(d) if that's the function defined on the whole dataset. But if he's only describe what g does outside of D, then it's a totally valid target function. Let me ask my question a different way; perhaps that will be clearer. For 6(d), is g[0,0,0] = 0 or is g[0,0,0]=1? 
Re: Confused on question 6.
"We want to determine the hypothesis that agrees the most with the possible target functions." and we are measuring this by counting how many of the 3 points not in D, agree with the hypothesis for each of the 8 target functions. In 6(a) & 6(b), the hypothesis is only defined on the last three points. Although 6(c) & (d) are not, it is known to us what f(x) is for points in D. So I think you are more interested in g[1,1,1], g[1,1,0], g[1,0,1].

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I still don't think I'm interpreting this question correctly.
For 6(d), the function described does not match the data set D. So, given that, am I correct in thinking that for hypothesis 6(d) there are zero target functions that match the hypothesis? Because, by definition, a target function must agree with the given data set D. Right? 
Re: Confused on question 6.
Yes. the target function agrees with D and there are 8 of them.
Now we want to determine the hypothesis that agrees the most with the possible target functions. Problem 6 defines this measurement as counting how many of the target functions match with each hypothesis on the three points.:) 
Re: Confused on question 6.
I'm confused, were we supposed to work this out by hand or were we supposed to code it out?

Re: Confused on question 6.
I just started. Not sure if forum is closed or not. I have confusion too. As I understand hypothesis set is associated with a learning algorithm. does g in choice from a to d come from same learning algorithm or description represents different algorithm? Since we have 256 possible hypothesis, I can conceptually call my learning algorithm "try all" which have all 256 possible functions as its hypothesis. Does this exercise assume we are working with "try all" algorithm?.
Thanks, 
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To answer your question, the algorithm can try all hypotheses (in the hypothesis set), but it will have to choose one and only one as the final hypothesis that it reports. When we grade the algorithm, what matters is the performance of the final hypothesis it arrived at, regardless of how it arrived at it. 
Re: Confused on question 6.
It's taking me a while to get my head around whats going on in this question and how I am supposed to calculate the scores.
For a) , the hypothesis g returns 1 for all three points. So does this mean that for each of the points 101,110 and 111 as x_n, then y_n is 1 ? If so then I am not sure what I am then supposed to compare this to? Thanks for any help. 
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Re: Confused on question 6.
Thanks for the quick reply.
I've only just realised that the fact I've done very little Boolean other than knowing what the basic gates are is making this confusing for me? I did some further reading, but it's hard to find a quick summary? Sorry to be asking dumb questions but using AND, OR and NOT I get 9 possible functions instead of 8: a+b+c a+b*c a*b*c a*b+c a'b'c a'b+c a+b'c a*b'c a'b*c Is there something straight forward thats wrong about this or do I need to go and spend an evening learning these before moving on?! 
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Re: Confused on question 6.
Could you post the question in an *ANSWER* thread (see above "BEFORE posting answers  please read").

Re: Confused on question 6.
Sorry, deleted.
Will post under the correct thread. 
Re: Confused on question 6.
This is exactly what I am going to ask also :D

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