Learning with Complex Loss Functions and Constraints

Harikrishna Narasimhan
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:1646-1654, 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, non-linear loss functions such as the F-measure, G-mean or H-mean, 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 cost-sensitive learning tasks. We provide algorithms for two broad families of problems, involving convex and fractional-convex 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v84-narasimhan18a, title = {Learning with Complex Loss Functions and Constraints}, author = {Narasimhan, Harikrishna}, booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics}, pages = {1646--1654}, year = {2018}, editor = {Storkey, Amos and Perez-Cruz, Fernando}, volume = {84}, series = {Proceedings of Machine Learning Research}, month = {09--11 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v84/narasimhan18a/narasimhan18a.pdf}, url = {https://proceedings.mlr.press/v84/narasimhan18a.html}, 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, non-linear loss functions such as the F-measure, G-mean or H-mean, 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 cost-sensitive learning tasks. We provide algorithms for two broad families of problems, involving convex and fractional-convex 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.} }
Endnote
%0 Conference Paper %T Learning with Complex Loss Functions and Constraints %A Harikrishna Narasimhan %B Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2018 %E Amos Storkey %E Fernando Perez-Cruz %F pmlr-v84-narasimhan18a %I PMLR %P 1646--1654 %U https://proceedings.mlr.press/v84/narasimhan18a.html %V 84 %X 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, non-linear loss functions such as the F-measure, G-mean or H-mean, 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 cost-sensitive learning tasks. We provide algorithms for two broad families of problems, involving convex and fractional-convex 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.
APA
Narasimhan, H.. (2018). Learning with Complex Loss Functions and Constraints. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 84:1646-1654 Available from https://proceedings.mlr.press/v84/narasimhan18a.html.

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