Confused on question 6.

[ArikB]

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:

101 | 1
110 | 1
111 | 1

And g[b], returns all 0's:

101 | 0
110 | 0
111 | 0

And g[c], the xor function, would return:

101 | 0
110 | 0
111 | 1

and g(d), inverse of g(c), would return:

101 | 1
110 | 1
111 | 0

Or could it be that g[1] means that it will only return a 1 if all points are 1? So:

101 | 0
110 | 0
111 | 1

and g[b] would have a score of 0, because there are no 000 points.

I'm utterly confused by the question. :/

[yaser]

Originally Posted by ArikB

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?

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.

[ArikB]

Originally Posted by yaser

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.

Thank you for the response, I was approaching the question completely wrong but solved it in the meantime.

[yaser]

Originally Posted by ArikB

Thank you for the response, I was approaching the question completely wrong but solved it in the meantime.

You are welcome. Everyone is encouraged to ask questions, big or small.

[noahdavis]

Originally Posted by yaser

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.

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.

[yaser]

Originally Posted by noahdavis

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.

Possible target function is a notion introduced in this problem in order to make a point about learning. In general, there is one target function, albeit unknown. Here we spell out "unkown" by considering all the possibilities the target function can assume. We can afford to do that here because there is only a finite number of possibilities.

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.

[noahdavis]

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.

[kumarpiyush]

Originally Posted by noahdavis

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.

Does this mean the combinations of (000) ,(001) upto (111) are the 8 target functions?

[kumarpiyush]

Originally Posted by yaser

Possible target function is a notion introduced in this problem in order to make a point about learning. In general, there is one target function, albeit unknown. Here we spell out "unkown" by considering all the possibilities the target function can assume. We can afford to do that here because there is only a finite number of possibilities.

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.

I understood it now :-)

[lhamilton]

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?