Optimistic bounds for multi-output prediction

17 September 2020, 9.00 AM - 17 September 2020, 10.00 AM

Henry Reeve, University of Bristol Via Zoom

About the speakers

Henry Reeve was recently appointed as a Lecturer in Statistical Science at the University of Bristol. Previously, he worked as a Machine Learning Research Fellow as with Ata Kaban at the University of Birmingham. Henry holds a PhD in Pure Mathematics from the University of Bristol, supervised by Thomas Jordan. After leaving Bristol he worked in finance for several years in Sydney before returning to the UK to obtain a PhD in Computer Science at the University of Manchester, under the supervision of Gavin Brown. His current research interests focus on the intersection between Statistics and Machine Learning with a focus upon non-parametric and weakly supervised learning. 

About the seminars

Optimistic bounds for multi-output prediction

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 a geometric 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. An important example arises when we have a multi-label classification problem with sparse label vectors. We show that the self-bounding Lipschitz condition gives rise to optimistic bounds for multi-output learning, which are minimax optimal 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 generalization bound for multi-class gradient boosting. This is a joint work with Professor Ata Kaban at the University of Birmingham. 



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Data Science Seminars

This seminar is part of a weekly series of seminars bringing together academics form the Institute of Statistical Mathematics in Japan and the University of Bristol to foster collaborations in geometric data analysis. 

Take a look at Data Science Seminars - The Institue of Statistical Mathematics, Japan and University of Bristol for details of the full programme of seminars.

Find out more about our partnership with The Institute of Statistical Mathematics in Japan.

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