I got two questions.
1.
I know that in predictive analytics contests, when faced to yes/no problems, with the absolute cost function
$f(x) = \frac{1}{n}\sum_{i=1}^n\lvert x_i-\hat x_i\rvert$
the best approach is to give
$1\ if\ \hat x_i>=0.5$
or
$0\ if\ \hat x_i <0.5$
Does anyone know a nice formal prove for it?
2.
In general, do you know any readable articles on the best approach to different cost functions (such as MSE and so on...)?