We study surrogate losses in the context of cost-sensitive classification with example-dependent costs, a problem also known as regression level set estimation. We give sufficient conditions on the surrogate loss for the existence of a surrogate regret bound. Such bounds imply that as the surrogate risk tends to its optimal value, so too does the expected misclassification cost. Our sufficient conditions encompass example-dependent versions of the hinge, exponential, and other common losses. These results provide theoretical justification for some previously proposed surrogate-based algorithms, and suggests others that have not yet been developed.
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