Still unclear on Problem 6

[ripande]

For some reason I am still confused about what question 6 demands. I have read Prof Yaser's reply to the earlier post regarding this question, but I still dont get it.

a). As I understand, a possible target function is the one that agrees with all the 5 points that are stated in the problem.

b). However, the questions says that the possible target functions are 8 ( all permulations of the remaining 3 points with their possible outputs ).

I am unable to relate the above two definitions of the "possible target function".

[yaser]

Originally Posted by ripande

a). As I understand, a possible target function is the one that agrees with all the 5 points that are stated in the problem.

b). However, the questions says that the possible target functions are 8 ( all permulations of the remaining 3 points with their possible outputs ).

I am unable to relate the above two definitions of the "possible target function".

A target function is defined on all 8 points. To be a possible target function given that it generated the data set of 5 points, it has to agree with these points since it generated them. This leaves 3 points which can assume any values and still make the function a possible target function. Since there are 8 possible combinations of values on these 3 points, this gives us 8 distinct functions all of which are possible target functions.

[butterscotch]

Let's say the hypothesis is "returns 0 for all three points".
The following target function is defined on 8 points, agrees with the hypothesis, and agrees with D.
[ x_n; y_n]
[0,0,0;0]
[0,0,1;1]
[0,1,0;1]
[0,1,1;0]
[1,0,0;1]
[1,0,1;0]
[1,1,0;0]
[1,1,1;0]

---------------------------------------------
[ x_n; y_n]
[0,0,0;0]
[0,0,1;0]
[0,1,0;1]
[0,1,1;0]
[1,0,0;1]
[1,0,1;0]
[1,1,0;0]
[1,1,1;0]

also agrees with the hypothesis, but it does not agree with D, hence not one of the 8 target functions.

[ripande]

Understood. :-) Thanks Prof Yaser and Butterscotch