loss_function.md

損失函數

下表概述了MLlib支持的損失函數及其梯度和子梯度：

	損失函數$$L(w;x,y)$$	梯度或子梯度
hinge loss	$$max{0, 1-yw^Tx} $$	$$ \left{ \begin{array}{ll} -yx ~~~ 若~yw^Tx \lt1, \ 0 ~~~~~~~~~otherwise \end{array} \right.$$
logistic loss	$$log(1+exp(-yw^Tx)),~y \in {-1,+1}$$	$$-y(1-\frac{1}{1+exp(-yw^Tx)})x$$
squared loss	$$\frac{1}{2}(x^Tx-y)^2,~y \in R$$	$$(w^Tx-y)x$$