Active Sampling over Graphs for Bayesian Reconstruction with Gaussian Ensembles

Graph-guided semi-supervised learning (SSL) has gained popularity in several network science applications, including biological, social, and financial ones. SSL becomes particularly challenging when the available nodal labels are scarce, what motivates naturally the active learning (AL) paradigm. AL seeks the most informative nodes to label in order to effectively estimate the nodal values of unobserved nodes. It is also referred to as active sampling, and boils down to learning the sought function mapping, and an acquisition function (AF) to identify the next node(s) to sample. To learn the mapping, this work leverages an adaptive Bayesian model comprising an ensemble (E) of Gaussian Processes (GPs) with enhanced expressiveness of the function space. Unlike most alternatives, the EGP model relies only on the one-hop connectivity of each node. Capitalizing on this EGP model, a suite of novel and intuitive AFs are developed to guide the active sampling process. These AFs are then combined with weights that are adapted incrementally to further robustify performance. Numerical tests on real and synthetic datasets corroborate the merits of the novel methods.