UCLA

We present various results and methods for measuring uncertainty and applying active learning to graph-based semi-supervised learning, as well as a graph-dependent result for generalization of decentralized federated learning. The first piece of work presents an analysis of graph-based semi-supervised learning in the framework of Bayesian inverse problems; we prove posterior consistency of the corresponding Bayesian posterior distribution under a clustering model that accounts for overlap between clusters. The second and third pieces of work introduce and apply a graph-based method for selecting informative points for use in active learning. We present a computationally efficient framework for this active learning method and present empirical results on both hyperspectral and synthetic aperture radar datasets. The final piece of work provides an analysis of graph structure dependent generalization guarantees for decentralized federated learning. Through both theoretical analysis and empirical results, we demonstrate that expander graphs are in a sense optimally efficient for balancing communication cost as well as mixing properties of the associated graph.