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SaPHyRa: A Learning Theory Approach to Ranking Nodes in Large Networks

Ranking nodes based on their centrality stands a fundamental, yet, challenging problem in large-scale networks. Approximate methods can quickly estimate nodes' centrality and identify the most central nodes, but the ranking for the majority of remaining nodes may be meaningless. For example, ranking for less-known websites in search queries is known to be noisy and unstable. To this end, we investigate a new node ranking problem with two important distinctions: a) ranking quality, rather than the centrality estimation quality, as the primary objective; and b) ranking only nodes of interest, e.g., websites that matched search criteria. We propose Sample space Partitioning Hypothesis Ranking, or SaPHyRa, that transforms node ranking into a hypothesis ranking in machine learning. This transformation maps nodes' centrality to the expected risks of hypotheses, opening doors for theoretical machine learning (ML) tools. The key of SaPHyRa is to partition the sample space into exact and approximate subspaces. The exact subspace contains samples related to the nodes of interest, increasing both estimation and ranking qualities. The approximate space can be efficiently sampled with ML-based techniques to provide theoretical guarantees on the estimation error. Lastly, we present SaPHyRa_bc, an illustration of SaPHyRa on ranking nodes' betweenness centrality (BC). By combining a novel bi-component sampling, a 2-hop sample partitioning, and improved bounds on the Vapnik-Chervonenkis dimension, SaPHyRa_bc can effectively rank any node subset in BC. Its performance is up to 200x faster than state-of-the-art methods in approximating BC, while its rank correlation to the ground truth is improved by multifold.