Title: Doing More with Less: Graph-based Methods for Learning from Limited Observations
Abstract: Modern research in machine learning has primarily focused on the supervised learning of functions from massive amounts of labeled data, where inputs with their observed outputs (labels) are available to the learning algorithm. However, in applications, it is often more realistic to have plenty of unlabeled data (i.e., inputs without known labels) while only few labeled data. With a common theme of leveraging the geometric structure of data through similarity graphs, I will present my recent work on the theoretical understanding and computational application of semi-supervised and active learning paradigms for learning when labeled data are scarce but unlabeled data are plentiful. I will discuss my work to prove Bayesian posterior contraction in graph-based semi-supervised regression and how it inspired the subsequent design of a computationally efficient graph-based active learning method. I will also present a novel uncertainty sampling criterion for active learning in a graph-based model that has a well-defined continuum limit partial differential equation formulation; this continuum limit model facilitates the establishment of rigorous mathematical guarantees about the sampling complexity of the proposed method. Experimental results will demonstrate the utility of the methods to various applications like pixel classification in hyperspectral imagery and automatic target recognition in synthetic aperture radar imagery.