#1




Problem 1.12a
I'm somewhat lost in my attempt to show 1.12 a I can see intuitively that the mean will be the best h value since then Ein is the standard deviation, but I'm not sure where to go from there. I've already finished B and C, A is the only part I'm having trouble with.
Perhaps I'm going in the wrong direction but one of the things I realized is that the constraint could be restated as minimizing h^2 2 h yn summed over all N but that could be going off in completely the wrong direction. Adding some value a to the mean produces (meanyn)^2 + a^2 +2 a(meanyn) That's another possible approach but I'm not really sure where I would take that approach either. 
#2




Re: Problem 1.12a
Quote:
To start off work on factoring out h, then it should become more obvious how to manipulate the function to find its minimum value. Good luck! 
#3




Re: Problem 1.12a
I tried to take the derivative of the function to find the minimum, but I'm still not sure how the minimum corresponds to h being the insample mean.
Also, what exactly is hmean? It seems to be a scalar value, a number of some sort, but I thought that h is a hypothesis/function? 
#4




Re: Problem 1.12a
This is the right idea. Your hypothesis h is just a number in this case. Ein is a function of this number (variable) h. One way to minimize a function of a variable h is to take the derivative and set it to zero.
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