Nonlocal operators with heterogeneous localization with applications to semi-supervised learning

Data Science Seminar

Qiang Du
Columbia University

Abstract

Recent applications and theoretical developments of models of integral equations using nonlocal operators have shown promise as effective alternatives to local models, especially in the presence of singularities and anomalies. For such models defined on a bounded domain, we present the heterogeneous localization technique to impose local boundary conditions. This can be useful for the seamless coupling of local and nonlocal models and for developing well-defined nonlocal models for semi-supervised learning with low labeling rates, thus providing analytical bridges linking discrete learning models and PDE-based local continuum models.