#### Conference abstracts

Session B4 - Learning Theory

July 14, 15:00 ~ 15:25

## Consistency and comparison of objective functionals in semi-supervised learning

### Dejan Slepcev

### Carnegie Mellon University, United States - slepcev@math.cmu.edu

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 distinct 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.

Joint work with Matthew Dunlop (Caltech), Andrew Stuart (Caltech) and Matthew Thorpe (CMU).