Given a set of N {\displaystyle N} training examples of the form { ( x 1 , y 1 ) , . . . , ( x N , y N ) } {\displaystyle \{(x_{1},y_{1}),...,(x_{N},\;y_{N})\}} such that x i {\displaystyle x_{i}} is the feature vector of the i-th example and y i {\displaystyle y_{i}} is its label (i.e., class), a learning algorithm seeks a function g : X → Y {\displaystyle g:X\to Y} , where X {\displaystyle X} is the input space and Y {\displaystyle Y} is the output space. The function g {\displaystyle g} is an element of some space of possible functions G {\displaystyle G} , usually called the hypothesis space. It is sometimes convenient to represent g {\displaystyle g} using a scoring function f : X × Y → R {\displaystyle f:X\times Y\to {\mathbb {R}}} such that g {\displaystyle g} is defined as returning the y {\displaystyle y} value that gives the highest score: g ( x ) = arg ⁡ max y f ( x , y ) {\displaystyle g(x)=\arg \max _{y}\;f(x,y)} .