Abstract: Graph-based semi-supervised learning is a field within machine learning that uses both labeled and unlabeled data with an underlying graph structure for classification and regression tasks. In problems where very little labeled data is available, the classical Laplacian regularization gives very poor results. This can be explained through its PDE continuum limit, which is an ill-posed elliptic equation. Much work recently has been focused on designing graph-based learning methods with well-posed continuum limits, including the p-Laplacian, higher order Laplacians, re-weighted Laplacians, and Poisson equations.

In this talk, we will survey this literature, and present our recent work on using Poisson equations for semi-supervised learning. We will present theoretical results which establish that learning with Poisson equations is provably well-posed at arbitrarily low label rates, and experimental results showing that it outperforms existing graph-based semi-supervised learning methods on challenging data sets. We will also present some recent work on applications of Poisson learning to graph-based active learning, where the goal is to select a training set with the most informative examples, often in a sequential online setting starting at extremely low label rates.

Event will be in-person and on Zoom: https://umich.zoom.us/j/98734707290

Contact: Selim Esedoglu