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Learning Globally Smooth Functions on Manifolds
Juan Cervino · Luiz Chamon · Benjamin Haeffele · Rene Vidal · Alejandro Ribeiro

Thu Jul 27 01:30 PM -- 03:00 PM (PDT) @ Exhibit Hall 1 #134

Smoothness and low dimensional structures play central roles in improving generalization and stability in learning and statistics. This work combines techniques from semi-infinite constrained learning and manifold regularization to learn representations that are globally smooth on a manifold. To do so, it shows that under typical conditions the problem of learning a Lipschitz continuous function on a manifold is equivalent to a dynamically weighted manifold regularization problem. This observation leads to a practical algorithm based on a weighted Laplacian penalty whose weights are adapted using stochastic gradient techniques. It is shown that under mild conditions, this method estimates the Lipschitz constant of the solution, learning a globally smooth solution as a byproduct. Experiments on real world data illustrate the advantages of the proposed method relative to existing alternatives. Our code is available at https://github.com/JuanCervino/smoothbench.

Author Information

Juan Cervino (University Of Pennsylvania)
Juan Cervino

Juan received the B.Sc. degree in electrical engineering from the Universidad de la Republica Oriental del Uruguay, Montevideo, in 2018. He is now a PhD student in the Department of Electrical and Systems Engineering at the University of Pennsylvania, supervised by Professor Alejandro Ribeiro. Juan's current research interests are in machine learning, optimization and control.

Luiz Chamon (University of California, Berkeley)
Benjamin Haeffele (Johns Hopkins University)
Rene Vidal (University of Pennsylvania)
Alejandro Ribeiro (University of Pennsylvania)

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