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Consistency of objective functionals in semi-supervised learning

Banff International Research Station for Mathematical Innovation and Discovery

We consider a regression problem of semi-supervised learning: given real-valued labels on a small subset of data recover the function on the whole data set while taking into account the information provided by a large number of unlabeled data points. Objective functionals modeling this regression problem involve terms rewarding the regularity of the function estimate while enforcing agreement with the labels provided. We will discuss and prove which of these functionals make sense when the number of data points goes to infinity. Furthermore we will discuss qualitative properties of function estimates that different regularizations lead to. In particular we will discuss regularizations motivated by p-Laplace equation and higher order fractional Laplacians. The talk is based on joint work with Matthew Dunlop, Andrew Stuart, and Matthew Thorpe.

Mathematics; Calculus of variations and optimal control; optimization; Statistics; Scientific computing

video/mp4

Author affiliation: Carnegie Mellon University

2017-10-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63469

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/