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.
|Number of pages||11|
|Journal||Proceedings of Machine Learning Research|
|Publication status||Published - 19 Mar 2021|
|Event||37th International Conference on Machine Learning (ICML 2020) - |
Duration: 12 Jul 2020 → 18 Jul 2020