The Geometry and Calculus of Losses

Statistical decision problems lie at the heart of statistical machine learning. The simplest problems are multiclass classification and class probability estimation. Central to their definition is the choice of loss function, which is the means by which the quality of a solution is evaluated. In this paper we systematically develop the theory of loss functions for such problems from a novel perspective whose basic ingredients are convex sets with a particular structure. The loss function is defined as the subgradient …

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