Machine Learning Seminar Series

Poisson learning: Graph-based semi-supervised learning at very low label rates


Jeff Calder
School of Mathematics
University of Minnesota

Wednesday, September 30, 2020
3:30–4:30 pm

View the recording here

Download the presentation slides (pdf 12.5 MB)

Graph-based learning is a field within machine learning that uses similarities between datapoints to create efficient representations of high-dimensional data for tasks like semi-supervised classification, clustering and dimension reduction. For semi-supervised learning, the widely used Laplacian regularizer has recently been shown to be ill-posed at very low label rates, leading to poor classification similar to random guessing. In this talk, we will give a careful analysis of the ill-posedness of Laplacian regularization via random walks on graphs, and this will lead to a new algorithm for semi-supervised learning that we call Poisson learning. Poisson learning replaces the assignment of label values at training points with the placement of sources and sinks, and solves the resulting Poisson equation on the graph. The outcomes are provably more stable and informative than those of Laplacian learning. Poisson learning is efficient and simple to implement, and we will present numerical results on MNIST, FashionMNIST and Cifar-10 showing that the method is superior to other recent approaches to semi-supervised learning at low label rates.

This talk is joint work with Brendan Cook (UMN), Dejan Slepcev (CMU) and Matthew Thorpe (University Manchester).

Jeff Calder is an assistant professor of mathematics at the University of Minnesota. He completed his PhD in 2014 at the University of Michigan advised by Selim Esedoglu (Math) and Alfred Hero (EECS), and was a Morrey assistant professor at UC Berkeley from 2014-2016. Calder was awarded an Alfred P. Sloan Research Fellowship in 2020. His research interests are focused on the intersection of partial differential equations, machine learning, and applied probability.