Loss functions for classification

In machine learning and mathematical optimization, loss functions for classification are computationally feasible loss functions representing the price paid for inaccuracy of predictions in classification problems (problems of identifying which category a particular observation belongs to). Given X {\displaystyle {\mathcal {X}}} as the space of all possible inputs (usually X ⊂ R d {\displaystyle {\mathcal {X}}\subset \mathbb {R} ^{d}} ), and Y = { − 1 , 1 } {\displaystyle {\mathcal {Y}}=\{-1,1\}} as the set of labels (possible outputs), a typical goal of classification algorithms is to find a function f : X → Y {\displaystyle f:{\mathcal {X}}\to {\mathcal {Y}}} which best predicts a label y {\displaystyle y} for a given input x → {\displaystyle {\vec {x}}} .

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