Learning with Complex Loss Functions and Constraints
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Proceedings of the TwentyFirst International Conference on Artificial Intelligence and Statistics, PMLR 84:16461654, 2018.
Abstract
We develop a general approach for solving constrained classification problems, where the loss and constraints are defined in terms of a general function of the confusion matrix. We are able to handle complex, nonlinear loss functions such as the Fmeasure, Gmean or Hmean, and constraints ranging from budget limits, to constraints for fairness, to bounds on complex evaluation metrics. Our approach builds on the framework of Narasimhan et al. (2015) for unconstrained classification with complex losses, and reduces the constrained learning problem to a sequence of costsensitive learning tasks. We provide algorithms for two broad families of problems, involving convex and fractionalconvex losses, subject to convex constraints. Our algorithms are statistically consistent, generalize an existing approach for fair classification, and readily apply to multiclass problems. Experiments on a variety of tasks demonstrate the efficacy of our methods.
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