Optimistic Bounds for Multi-output Prediction

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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 multioutput 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.
Original languageEnglish
Pages (from-to)8030-8040
Number of pages11
JournalProceedings of Machine Learning Research
Publication statusPublished - 19 Mar 2021
Event37th International Conference on Machine Learning (ICML 2020) -
Duration: 12 Jul 202018 Jul 2020

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