In many supervised learning problems one has an output variable y and a vector of input variables x described via a joint probability distribution P ( x , y ) {\displaystyle P(x,y)} . Using a training set { ( x 1 , y 1 ) , … , ( x n , y n ) } {\displaystyle \{(x_{1},y_{1}),\dots ,(x_{n},y_{n})\}} of known values of x and corresponding values of y, the goal is to find an approximation F ^ ( x ) {\displaystyle {\hat {F}}(x)} to a function F ( x ) {\displaystyle F(x)} that minimizes the expected value of some specified loss function L ( y , F ( x ) ) {\displaystyle L(y,F(x))} :