Optimistic Bounds for Multi-output Learning

Henry Reeve, Ata Kaban
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:8030-8040, 2020.

Abstract

We investigate the challenge of multi-output learning, where the goal is to learn a vector-valued function based on a supervised data set. This includes a range of important problems in Machine Learning including multi-target regression, multi-class classification and multi-label classification. We begin our analysis by introducing the self-bounding Lipschitz condition for multi-output loss functions, which interpolates continuously between a classical Lipschitz condition and a multi-dimensional analogue of a smoothness condition. We then show that the self-bounding Lipschitz condition gives rise to optimistic bounds for multi-output learning, which attain the minimax optimal rate up to logarithmic factors. The proof exploits local Rademacher complexity combined with a powerful minoration inequality due to Srebro, Sridharan and Tewari. As an application we derive a state-of-the-art generalisation bound for multi-class gradient boosting.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-reeve20a, title = {Optimistic Bounds for Multi-output Learning}, author = {Reeve, Henry and Kaban, Ata}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {8030--8040}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/reeve20a/reeve20a.pdf}, url = {https://proceedings.mlr.press/v119/reeve20a.html}, abstract = {We investigate the challenge of multi-output learning, where the goal is to learn a vector-valued function based on a supervised data set. This includes a range of important problems in Machine Learning including multi-target regression, multi-class classification and multi-label classification. We begin our analysis by introducing the self-bounding Lipschitz condition for multi-output loss functions, which interpolates continuously between a classical Lipschitz condition and a multi-dimensional analogue of a smoothness condition. We then show that the self-bounding Lipschitz condition gives rise to optimistic bounds for multi-output learning, which attain the minimax optimal rate up to logarithmic factors. The proof exploits local Rademacher complexity combined with a powerful minoration inequality due to Srebro, Sridharan and Tewari. As an application we derive a state-of-the-art generalisation bound for multi-class gradient boosting.} }
Endnote
%0 Conference Paper %T Optimistic Bounds for Multi-output Learning %A Henry Reeve %A Ata Kaban %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-reeve20a %I PMLR %P 8030--8040 %U https://proceedings.mlr.press/v119/reeve20a.html %V 119 %X We investigate the challenge of multi-output learning, where the goal is to learn a vector-valued function based on a supervised data set. This includes a range of important problems in Machine Learning including multi-target regression, multi-class classification and multi-label classification. We begin our analysis by introducing the self-bounding Lipschitz condition for multi-output loss functions, which interpolates continuously between a classical Lipschitz condition and a multi-dimensional analogue of a smoothness condition. We then show that the self-bounding Lipschitz condition gives rise to optimistic bounds for multi-output learning, which attain the minimax optimal rate up to logarithmic factors. The proof exploits local Rademacher complexity combined with a powerful minoration inequality due to Srebro, Sridharan and Tewari. As an application we derive a state-of-the-art generalisation bound for multi-class gradient boosting.
APA
Reeve, H. & Kaban, A.. (2020). Optimistic Bounds for Multi-output Learning. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:8030-8040 Available from https://proceedings.mlr.press/v119/reeve20a.html.

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