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Learning with Invariance via Linear Functionals on Reproducing Kernel Hilbert Space
Xinhua Zhang · Wee Sun Lee · Yee Whye Teh

Sat Dec 07 11:40 AM -- 11:44 AM (PST) @ Harvey's Convention Center Floor, CC

Incorporating invariance information is important for many learning problems. To exploit invariances, most existing methods resort to approximations that either lead to expensive optimization problems such as semi-definite programming, or rely on separation oracles to retain tractability. Some methods further limit the space of functions and settle for non-convex models. In this paper, we propose a framework for learning in reproducing kernel Hilbert spaces (RKHS) using local invariances that explicitly characterize the behavior of the target function around data instances. These invariances are \emph{compactly} encoded as linear functionals whose value are penalized by some loss function. Based on a representer theorem that we establish, our formulation can be efficiently optimized via a convex program. For the representer theorem to hold, the linear functionals are required to be bounded in the RKHS, and we show that this is true for a variety of commonly used RKHS and invariances. Experiments on learning with unlabeled data and transform invariances show that the proposed method yields better or similar results compared with the state of the art.

Author Information

Xinhua Zhang (University of Illinois at Chicago (UIC))
Wee Sun Lee (National University of Singapore)

Wee Sun Lee is a professor in the Department of Computer Science, National University of Singapore. He obtained his B.Eng from the University of Queensland in 1992 and his Ph.D. from the Australian National University in 1996. He has been a research fellow at the Australian Defence Force Academy, a fellow of the Singapore-MIT Alliance, and a visiting scientist at MIT. His research interests include machine learning, planning under uncertainty, and approximate inference. His works have won the Test of Time Award at Robotics: Science and Systems (RSS) 2021, the RoboCup Best Paper Award at International Conference on Intelligent Robots and Systems (IROS) 2015, the Google Best Student Paper Award, Uncertainty in AI (UAI) 2014 (as faculty co-author), as well as several competitions and challenges. He has been an area chair for machine learning and AI conferences such as the Neural Information Processing Systems (NeurIPS), the International Conference on Machine Learning (ICML), the AAAI Conference on Artificial Intelligence (AAAI), and the International Joint Conference on Artificial Intelligence (IJCAI). He was a program, conference and journal track co-chair for the Asian Conference on Machine Learning (ACML), and he is currently the co-chair of the steering committee of ACML.

Yee Whye Teh (University of Oxford, DeepMind)

I am a Professor of Statistical Machine Learning at the Department of Statistics, University of Oxford and a Research Scientist at DeepMind. I am also an Alan Turing Institute Fellow and a European Research Council Consolidator Fellow. I obtained my Ph.D. at the University of Toronto (working with Geoffrey Hinton), and did postdoctoral work at the University of California at Berkeley (with Michael Jordan) and National University of Singapore (as Lee Kuan Yew Postdoctoral Fellow). I was a Lecturer then a Reader at the Gatsby Computational Neuroscience Unit, UCL, and a tutorial fellow at University College Oxford, prior to my current appointment. I am interested in the statistical and computational foundations of intelligence, and works on scalable machine learning, probabilistic models, Bayesian nonparametrics and deep learning. I was programme co-chair of ICML 2017 and AISTATS 2010.

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