# Data Mining - Minimizer of the risk

To show

Given: $$Loss(y, \hat{y}) = \alpha (\hat{y}-y)_+ + \beta (y-\hat{y})_+$$ Note: $$c_+$$ is equal to c if c > 0 and zero otherwise!

Show that the minimizer of the risk $$l(g) = E Loss(Y, g(X))$$ satisfies: $$P[Y where $$g^* (x)$$ is the optimal prediction function, that is $$g^* (x)=argmin_{g \in G} l(g)$$ in function class $$G$$

Progress

I interpret that $$g^* (x)$$ is the $$\frac{\beta}{\alpha + \beta}$$ quantile of Y conditional on $$X = x$$.

I'm uncertain about how to set up the probability distribution correctly and where to go from there.

Please comment if something is unclear. I'm just trying to learn!