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The advent of diverse frequency bands in 5G networks has promoted measurement studies focused on 5G signal propagation, aiming to understand its pathloss, coverage, and channel quality characteristics. Nonetheless, conducting a thorough 5G measurement campaign is markedly laborious given the large number of 5G measurement samples that must be collected. To alleviate this burden, the present contribution leverages principled active learning (AL) methods to prudently select only a few, yet most informative locations to collect 5G measurements. The core idea is to rely on a Gaussian Process (GP) model to efficiently extrapolate 5G measurements throughout the coverage area. Specifically, an ensemble (E) of GP models is adopted that not only provides a rich learning function space, but also quantifies uncertainty, and can offer accurate predictions. Building on this EGP model, a suite of acquisition functions (AFs) are advocated to query new locations on-the-fly. To account for realistic 5G measurement campaigns, the proposed AFs are augmented with a novel distance-based AL rule that selects informative samples, while penalizing queries at long distances. Numerical tests on 5G data generated by the Sionna simulator and on real urban and suburban datasets, showcase the merits of the novel EGP-AL approaches. 

Semi-supervised and unsupervised machine learning methods often rely on graphs to model data, prompting research on how theoretical properties of operators on graphs are leveraged in learning problems. While most of the existing literature focuses on undirected graphs, directed graphs are very important in practice, giving models for physical, biological or transportation networks, among many other applications. In this paper, we propose a new framework for rigorously studying continuum limits of learning algorithms on directed graphs. We use the new framework to study the PageRank algorithm and show how it can be interpreted as a numerical scheme on a directed graph involving a type of normalised graph Laplacian . We show that the corresponding continuum limit problem, which is taken as the number of webpages grows to infinity, is a second-order, possibly degenerate, elliptic equation that contains reaction, diffusion and advection terms. We prove that the numerical scheme is consistent and stable and compute explicit rates of convergence of the discrete solution to the solution of the continuum limit partial differential equation. We give applications to proving stability and asymptotic regularity of the PageRank vector. Finally, we illustrate our results with numerical experiments and explore an application to data depth.